Question 1

When one note is above another note by an octave,the frequency of the higher pitch note is double that of the lower pitch note.The word octave may make you think that there are 8 steps from the lower note to the one an octave above.But wait! How many steps are there on a piano from middle C to the next C above? Each key is a step.If each next key is a step,how many are there? Middle C is a white (W)key and the next note above is a black (B)key.Starting at middle C on the piano the sequence of key we go through to get to high C,is BWBWWBWBWBWW,the last key being high C.Count 'em.That's 12 steps.If the multiplying factor of the frequency for the next step is the same for each step,what is that multiplying frequency? All you need is given in this problem statement.

Accepted Answer

The multiplying factor is the twelfth root of 2 (2^(1/12)), because doubling the frequency corresponds to an octave, or 12 steps on the piano.

Question 2

A plane is traveling at Mach 0.980 through air at a temperature of 0°C.What is the plane's speed? (Speed of sound at 0°C is 331 m/s. )

Accepted Answer

Mach number is the ratio of the speed of an object to the speed of sound in the same medium. In this question, the plane is traveling at Mach 0.980 and the temperature of the air is 0°C, which means that the speed of sound is 331 m/s. Therefore, the plane's speed is calculated as follows: 
Plane speed = Mach number * speed of sound = 0.980 * 331 = 324.38 m/s. 
The closest option to this answer is B, 324 m/s.

Question 3

A sound source of frequency 1000 Hz moves at 40.0 m/s toward a listener who is at rest.What is the apparent frequency heard by the listener? (speed of sound = 340 m/s)

Accepted Answer

First, we need to determine the speed of the sound wave relative to the listener. This can be found by subtracting the speed of the observer from the speed of sound: 
340 m/s - 0 m/s (since the listener is at rest) = 340 m/s.

Next, we need to determine the frequency that the listener hears. We can use the Doppler effect equation:

f' = f (v + vo) / (v + vs)

Where: 
f = the frequency of the source 
v = the speed of sound 
vo = the velocity of the observer 
vs = the velocity of the source

Plugging in the values, we get:

f' = 1000 Hz (340 m/s + 0 m/s) / (340 m/s - 40.0 m/s) 
f' = 1130 Hz

Therefore, the apparent frequency heard by the listener is 1130 Hz, which is option C.

Question 4

A bat,flying at 3.00 m/s toward a wall,emits a chirp at 50.0 kHz.If the wall reflects this sound pulse,what is the frequency of the echo received by the bat? (v_sound = 340 m/s)

Accepted Answer

The frequency of the sound wave will not change upon reflection, only the direction in which it travels. However, the frequency perceived by the bat will be affected by the Doppler effect. 
Using the formula for the frequency observed by a stationary observer as a source moves towards or away from them: 
f' = (v + vo) / (v +/- vs) * f 
where 
f = frequency of source 
v = velocity of sound 
vo = velocity of observer (stationary for this problem) 
vs = velocity of source 
For the original chirp, f = 50.0 kHz and vs = -3.00 m/s (since it is moving towards the wall). Plugging in the values:
f' = (340 + 0) / (340 - (-3.00)) * 50.0 kHz = 50.9 kHz 
Therefore, the frequency of the echo received by the bat is 50.9 kHz. The correct choice is D.

Question 5

While standing at a crosswalk,you hear a frequency of 540 Hz from an approaching police car.After the police car passes,its frequency is 480 Hz.What is the speed of the police car? (speed of sound = 340 m/s)

Accepted Answer

The answer of While standing at a crosswalk,you hear a...

Question 6

Two cars,one in front of the other,are traveling down the highway at 25 m/s.The car behind sounds its horn,which has a frequency of 540 Hz.What is the frequency heard by the driver of the lead car? (v_sound = 340 m/s)

Accepted Answer

Since both cars are moving at the same speed, there is no relative motion between them, so the frequency heard by the driver of the lead car is the same as the frequency of the horn, 540 Hz.

Question 7

A 500-Hz whistle is moved toward a listener at a speed of 10.0 m/s.At the same time,the listener moves at a speed of 20.0 m/s in a direction toward the whistle.What is the apparent frequency heard by the listener? (The speed of sound is 340 m/s. )

Accepted Answer

The apparent frequency can be calculated using the Doppler effect formula: f' = f * (v + v_l) / (v - v_s), where f is the source frequency (500 Hz), v is the speed of sound (340 m/s), v_l is the speed of the listener (20 m/s), and v_s is the speed of the source (10 m/s). Plugging in the values, f' = 500 * (340 + 20) / (340 - 10) = 545 Hz.

Question 8

The Doppler shift of ultrasonic waves can measure the speed of blood in an artery.If the frequency of the stationary source is 100 kHz and the reflected sound has a Doppler shift of 300 Hz,what is the blood flow speed? (The speed of sound inside the body is 1500 m/s. )

Accepted Answer

The Doppler shift of sound wave can be expressed as:
Doppler shift = (2 * speed of blood * frequency of ultrasonic wave) / speed of sound inside the body
We can rearrange the formula to solve for the speed of blood:
Speed of blood = (Doppler shift * speed of sound inside the body) / (2 * frequency of ultrasonic wave)
Plugging in the given values, we get:
Speed of blood = (300 Hz * 1500 m/s) / (2 * 100 kHz) ≈ 2.25 m/s
Rounding off to the nearest tenth, we get 2.2 m/s as the blood flow speed, which is closest to option C.

Quiz 13: Vibrations and Waves: Part A