Question 1

A jet aircraft, in level flight at constant speed, is observed directly overhead. A sonic boom is heard 7.0 s later, at which time the line of sight to the aircraft forms a 56° angle with respect to the horizontal. The speed of sound is 325 m/s. What is the Mach number (the ratio of the speed of the jet to the speed of sound) for the aircraft?
A) 1.2
B) 1.8
C) 1.9
D) 2.1
E) 2.2

Accepted Answer

The answer of A jet aircraft, in level flight at...

Question 2

A carousel that is 5.00 m in radius has a pair of 600-Hz sirens mounted on posts at opposite ends of a diameter. The carousel rotates with an angular velocity of 0.800 rad/s. A stationary listener is located at a distance from the carousel. The speed of sound is 350 m/s. The maximum beat frequency of the sirens at the position of the listener is closest to
A) 6 Hz.
B) 8 Hz.
C) 10 Hz.
D) 12 Hz.
E) 14 Hz.

Accepted Answer

The answer of A carousel that is 5.00 m in...

Question 3

A carousel that is 5.00 m in radius has a pair of 600-Hz sirens mounted on posts at opposite ends of a diameter. The carousel rotates with an angular velocity of 0.800 rad/s. A stationary listener is located at a distance from the carousel. The speed of sound is 350 m/s. The longest wavelength reaching the listener from the sirens is closest to
A) 57.0 cm.
B) 57.7 cm.
C) 58.3 cm.
D) 59.0 cm.
E) 59.6 cm.

Accepted Answer

The frequency of the sound emitted by the sirens is 600 Hz. As the carousel rotates, one siren will be moving towards the listener while the other will be moving away. This causes a Doppler shift in the frequency of the sound heard by the listener. The frequency heard by the listener can be calculated using the formula:

f' = f (v +/- v_obs)/(v +/- v_s)

where f is the frequency of the sound emitted by the sirens, v is the speed of sound, v_obs is the speed of the observer (in this case, zero since the listener is stationary), and v_s is the speed of the source (in this case, the speed of the siren moving towards or away from the listener, depending on which siren is considered).

When the siren moving towards the listener is considered, the speed of the source is the sum of the speed of rotation of the carousel (v_r) and the speed of sound (v):

v_s = v_r + v

Substituting the given values, we get:

v_s = 0.800 rad/s x 5.00 m + 350 m/s = 354 m/s

When the siren moving away from the listener is considered, the speed of the source is the difference between the speed of rotation of the carousel (v_r) and the speed of sound (v):

v_s = v_r - v

Substituting the given values, we get:

v_s = 0.800 rad/s x 5.00 m - 350 m/s = -346 m/s

Using these values, we can calculate the frequencies heard by the listener:

f'_1 = 600 Hz (350 m/s + 0 m/s)/(350 m/s + 354 m/s) = 587.9 Hz
f'_2 = 600 Hz (350 m/s + 0 m/s)/(350 m/s - 346 m/s) = 9600 Hz

The longest wavelength that can be heard by the listener is when the frequency is at its lowest possible value, which occurs when the siren moving away from the listener is considered. The wavelength can be calculated using the formula:

lambda = v/f'

Substituting the calculated values, we get:

lambda = 350 m/s / 9600 Hz = 0.0365 m = 36.5 cm

However, the question asks for the longest wavelength reaching the listener, which occurs when the siren moving towards the listener is considered. Substituting the calculated values, we get:

lambda = 350 m/s / 587.9 Hz = 0.595 m = 59.5 cm

Therefore, the closest answer choice is D) 59.0 cm.

Question 4

An airplane flying faster than the speed of sound of 340 m/s produces a shock wave that makes an angle of 50° with the direction the plane is flying. What is the speed of the plane?
A) 490 m/s
B) 530 m/s
C) 390 m/s
D) 440 m/s
E) 405 m/s

Accepted Answer

The angle of the shock wave (θ) can be related to the Mach angle (μ) by the equation:

θ = arcsin(1/μ)

We are given that θ = 50° and the speed of sound is 340 m/s. Solving for μ, we get:

μ = 1/sin(50°) = 1.292

The speed of the plane (v) can then be found using the equation:

v = μ × speed of sound = 1.292 × 340 m/s ≈ 439.8 m/s ≈ 440 m/s

Therefore, the best choice is D.

Question 5

A supersonic plane passes overhead at a speed of 500 m/s. If you hear the sonic boom (shock wave) 4.00 s after the plane is directly overhead, at what altitude is the plane flying? Assume the speed of sound in air is 340 m/s.
A) 1.36 km
B) 2.16 km
C) 1.85 km
D) 2.45 km
E) The plane is not flying fast enough to produce a shock wave.

Accepted Answer

The speed of sound in air is 340 m/s. The plane is traveling at a speed of 500 m/s, which is greater than the speed of sound, so it produces a shock wave. The time delay between the plane passing overhead and the sonic boom being heard is 4.00 s.

Let's use the following equation to find the altitude of the plane:

d = vt

where d is the altitude, v is the speed of sound, and t is the time delay.

We know v = 340 m/s and t = 4.00 s, so:

d = (340 m/s)(4.00 s) = 1360 m = 1.36 km

Therefore, the plane is flying at an altitude of 1.36 km.

The correct answer is C.

Question 6

A jet aircraft, in level flight at constant speed, is observed directly over head. A sonic boom is heard 13.0 s later, at which time the line of sight to the aircraft forms a 51° angle with respect to the horizontal. The speed of sound is 325 m/s. The altitude of the aircraft is closest to
A) 6700 m.
B) 5400 m.
C) 8300 m.
D) 2700 m.
E) 13,000 m.

Accepted Answer

The aircraft is at an altitude of 6700 m.Explanation:The speed of the aircraft is:$$v = \frac{d}{t} = \frac{325 \ m/s 	imes 13.0 \ s}{\sin 51^\circ} = 425 \ m/s$$The altitude of the aircraft is:$$h = d 	an 51^\circ = 325 \ m/s 	imes 13.0 \ s 	imes 	an 51^\circ = 6700 \ m$$

Quiz 15: Sound and Hearing

An airplane flying faster than the speed of sound of 340 m/s produces a shock wave that makes an angle of 50° with the direction the plane is flying. What is the speed of the plane?

A supersonic plane passes overhead at a speed of 500 m/s. If you hear the sonic boom (shock wave) 4.00 s after the plane is directly overhead, at what altitude is the plane flying? Assume the speed of sound in air is 340 m/s.

A jet aircraft, in level flight at constant speed, is observed directly over head. A sonic boom is heard 13.0 s later, at which time the line of sight to the aircraft forms a 51° angle with respect to the horizontal. The speed of sound is 325 m/s. The altitude of the aircraft is closest to