Question 1

The wavelength of light visible to the human eye is on the order of 5 × 10−⁷ m. If the speed of light in air is 3 × 10⁸ m/s, find the frequency of the lightwave.

Accepted Answer

The frequency of a wave is calculated using the formula: frequency = speed of light / wavelength. Substituting the given values: frequency = (3 × 10^8 m/s) / (5 × 10^-7 m) = 6 × 10^14 Hz.

Question 2

For the transverse wave described by  , determine the maximum transverse speed of the particles of the medium.

Accepted Answer

The maximum transverse speed of particles in a transverse wave can be found using the equation:

v = Aω

where A is the amplitude of the wave and ω is the angular frequency.
From the given wave equation, we can see that the amplitude is 0.3 m and the angular frequency is 2π/T, where T is the period of the wave. We can find T using the equation:

T = 1/f

where f is the frequency of the wave. From the given wave equation, we can see that the wavelength is 0.8 m. We know that:

v = fλ

Solving for f:

f = v/λ

Substituting the given values:

f = 2/0.8 = 2.5 Hz

Substituting into the equation for T:

T = 1/f = 0.4 s

Substituting the values for A and ω into the equation for v:

v = Aω = (0.3 m)(2π/0.4 s) ≈ 1.88 m/s

However, this is the speed at which a single particle moves in the wave. The maximum transverse speed of the particles is twice this value:

v_max = 2v ≈ 3.76 m/s

Thus, the closest choice is B) 0.6π m/s, which is equivalent to 1.884956 m/s.

Question 3

If y = 0.02 sin (30x − 400t) (SI units), the angular frequency of the wave is

Accepted Answer

The angular frequency of a wave is given by the coefficient of $t$ in the argument of the sine function, which in this case is 400. Therefore, the angular frequency is $400 \, \text{rad/s}$.

Question 4

For the wave described by  , determine the x coordinate of the second maximum when t = 0.

Accepted Answer

The answer of For the wave described by  ,...

Question 5

Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/sec.

Accepted Answer

The general equation for a wave traveling along the +x axis can be written as y = A sin(kx − ωt + φ), where A is the amplitude, k is the wave number (2π/λ), ω is the angular frequency (2πf), t is time, and φ is the phase angle. Using the given values, we have:

A = 0.02 m
f = 440 Hz
v = 330 m/sec
λ = v/f = 330/440 = 0.75 m
k = 2π/λ = 8.38 m^−1
ω = 2πf = 880π rad/sec

Substituting these values into the general equation, we get:

y = 0.02 sin(8.38x − 880πt)

This matches with the equation given in choice A, y = 0.02 sin [880π(x/330 − t)]. Therefore, the answer is A.

Question 6

If y = 0.02 sin (30x − 400t) (SI units), the frequency of the wave is

Accepted Answer

The frequency of a wave in the form $y = A \sin(kx - \omega t)$ is given by $f = \frac{\omega}{2\pi}$. Here, $\omega = 400$, so the frequency $f = \frac{400}{2\pi} = \frac{200}{\pi}$ Hz.

Question 7

If y = 0.02 sin (30x − 400t) (SI units), the wavelength of the wave is

Accepted Answer

The wavelength $\lambda$ can be found from the wave equation $y = A \sin(kx - \omega t)$, where $k = \frac{2\pi}{\lambda}$. In the given equation, $30x - 400t$, comparing it to $kx - \omega t$, we find $k = 30$. Solving $30 = \frac{2\pi}{\lambda}$ for $\lambda$ gives $\lambda = \frac{2\pi}{30} = \frac{\pi}{15}$ meters.

Question 8

A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable is 3.00 × 10⁴ N, what is the speed of transverse waves on the cable?

Accepted Answer

The speed of transverse waves on a string or cable is given by the formula $v = \sqrt{\frac{T}{\mu}}$, where $v$ is the speed of the wave, $T$ is the tension in the cable, and $\mu$ is the mass per unit length (mass density) of the cable. Given $T = 3.00 \times 10^{4} \, \text{N}$ and $\mu = 2.01 \, \text{kg/m}$, we can calculate the speed as $v = \sqrt{\frac{3.00 \times 10^{4}}{2.01}} \approx 122 \, \text{m/s}$.

Question 9

The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.00-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire?

Accepted Answer

The answer of The lowest A on a piano has...

Question 10

Bats can detect small objects such as insects that are of a size on the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of soundwaves in air is 330 m/s, what is the smallest size insect they can detect?

Accepted Answer

The answer of Bats can detect small objects such as...

Question 11

Transverse waves are traveling on a 1.00-m long piano string at 500 m/s. If the points of zero vibration occur at one-half wavelength (where the string is fastened at both ends), find the frequency of vibration.

Accepted Answer

The wavelength is twice the length of the string, or 2.00 m. The frequency is the speed divided by the wavelength, or 500 m/s / 2.00 m = 250 Hz.

Question 12

If y = 0.02 sin (30x − 400t) (SI units) and if the mass density of the string on which the wave propagates is 0.005 kg/m, then the transmitted power is

Accepted Answer

The answer of If y = 0.02 sin (30x −...

Question 13

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave travels at 5 000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake center?

Accepted Answer

Let the distance between the seismic station and the earthquake center be "d".
Then, time taken by P-waves to travel from earthquake center to seismic station = d/9000
Time taken by S-waves to travel from earthquake center to seismic station = d/5000
Given that P-waves arrive 1 minute earlier than S-waves.
Therefore, d/9000 - d/5000 = 1
d = 675000 m = 675 km.

Question 14

Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?

Accepted Answer

The speed of the waves can be calculated using the formula: speed = wavelength × frequency. The frequency is 8 waves per minute, which is 8/60 waves per second. Therefore, speed = 120 m × (8/60) s⁻¹ = 16 m/s.

Question 15

A piano string of density 0.005 0 kg/m is under a tension of 1 350 N. Find the velocity with which a wave travels on the string.

Accepted Answer

The velocity of a wave on a string is given by the formula v = sqrt(T/μ), where T is the tension and μ is the linear density. Substituting the given values, v = sqrt(1350 / 0.005) = sqrt(270000) = 520 m/s.

Question 16

The speed of a 10-kHz sound wave in seawater is approximately 1 500 m/s. What is its wavelength in sea water?

Accepted Answer

The formula relating wavelength (λ), speed (v), and frequency (f) is: λ = v/f. 
Plugging in the given values: λ = 1500 m/s / 10,000 Hz = 0.15 m = 15 cm. Therefore, the wavelength of the 10-kHz sound wave in sea water is 15 cm. Choice C is the closest option at 15 cm.

Question 17

If y = 0.02 sin (30x − 400t) (SI units), the velocity of the wave is

Accepted Answer

The velocity of a wave, given by a function of the form $y = A \sin(kx - \omega t)$, can be found using the formula $v = \frac{\omega}{k}$, where $\omega$ is the angular frequency and $k$ is the wave number. In the given equation, $y = 0.02 \sin(30x - 400t)$, $\omega = 400$ and $k = 30$. Therefore, the velocity $v = \frac{400}{30} = \frac{40}{3}$ m/s.

Question 18

For the wave described by  , determine the first positive x coordinate where y is a maximum when t = 0.

Accepted Answer

The answer of For the wave described by  ,...

Question 19

For the wave described by y = 0.02 sin (kx) at t = 0 s, the first maximum at a positive x coordinate occurs where x = 4 m. Where on the positive x axis does the second maximum occur?

Accepted Answer

The answer of For the wave described by y =...

Question 20

If y = 0.02 sin (30x − 400t) (SI units), the wave number is

Accepted Answer

The wave number is given by the coefficient of x in the argument of the sine function when the equation is in the form of y = A sin(kx - ωt), where k is the wave number. In this case, k = 30 rad/m.

Quiz 16: Wave Motion

The wavelength of light visible to the human eye is on the order of 5 × 10−⁷ m. If the speed of light in air is 3 × 10⁸ m/s, find the frequency of the lightwave.

For the transverse wave described by , determine the maximum transverse speed of the particles of the medium.

If y = 0.02 sin (30x − 400t) (SI units) , the angular frequency of the wave is

For the wave described by , determine the x coordinate of the second maximum when t = 0.

Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/sec.

If y = 0.02 sin (30x − 400t) (SI units) , the frequency of the wave is

If y = 0.02 sin (30x − 400t) (SI units) , the wavelength of the wave is

A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable is 3.00 × 10⁴ N, what is the speed of transverse waves on the cable?

The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.00-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire?

Bats can detect small objects such as insects that are of a size on the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of soundwaves in air is 330 m/s, what is the smallest size insect they can detect?

Transverse waves are traveling on a 1.00-m long piano string at 500 m/s. If the points of zero vibration occur at one-half wavelength (where the string is fastened at both ends) , find the frequency of vibration.

If y = 0.02 sin (30x − 400t) (SI units) and if the mass density of the string on which the wave propagates is 0.005 kg/m, then the transmitted power is

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave travels at 5 000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake center?

Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?

A piano string of density 0.005 0 kg/m is under a tension of 1 350 N. Find the velocity with which a wave travels on the string.

The speed of a 10-kHz sound wave in seawater is approximately 1 500 m/s. What is its wavelength in sea water?

If y = 0.02 sin (30x − 400t) (SI units) , the velocity of the wave is

For the wave described by , determine the first positive x coordinate where y is a maximum when t = 0.

For the wave described by y = 0.02 sin (kx) at t = 0 s, the first maximum at a positive x coordinate occurs where x = 4 m. Where on the positive x axis does the second maximum occur?

If y = 0.02 sin (30x − 400t) (SI units) , the wave number is

Quiz 16: Wave Motion

The wavelength of light visible to the human eye is on the order of 5 × 10−7 m. If the speed of light in air is 3 × 108 m/s, find the frequency of the lightwave.

For the transverse wave described by , determine the maximum transverse speed of the particles of the medium.

If y = 0.02 sin (30x − 400t) (SI units) , the angular frequency of the wave is

For the wave described by , determine the x coordinate of the second maximum when t = 0.

Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/sec.

If y = 0.02 sin (30x − 400t) (SI units) , the frequency of the wave is

If y = 0.02 sin (30x − 400t) (SI units) , the wavelength of the wave is

A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable is 3.00 × 104 N, what is the speed of transverse waves on the cable?

The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.00-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire?

Bats can detect small objects such as insects that are of a size on the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of soundwaves in air is 330 m/s, what is the smallest size insect they can detect?

Transverse waves are traveling on a 1.00-m long piano string at 500 m/s. If the points of zero vibration occur at one-half wavelength (where the string is fastened at both ends) , find the frequency of vibration.

If y = 0.02 sin (30x − 400t) (SI units) and if the mass density of the string on which the wave propagates is 0.005 kg/m, then the transmitted power is

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave travels at 5 000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake center?

Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?

A piano string of density 0.005 0 kg/m is under a tension of 1 350 N. Find the velocity with which a wave travels on the string.

The speed of a 10-kHz sound wave in seawater is approximately 1 500 m/s. What is its wavelength in sea water?

If y = 0.02 sin (30x − 400t) (SI units) , the velocity of the wave is

For the wave described by , determine the first positive x coordinate where y is a maximum when t = 0.

For the wave described by y = 0.02 sin (kx) at t = 0 s, the first maximum at a positive x coordinate occurs where x = 4 m. Where on the positive x axis does the second maximum occur?

If y = 0.02 sin (30x − 400t) (SI units) , the wave number is

The wavelength of light visible to the human eye is on the order of 5 × 10−⁷ m. If the speed of light in air is 3 × 10⁸ m/s, find the frequency of the lightwave.

A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable is 3.00 × 10⁴ N, what is the speed of transverse waves on the cable?