Question 1

Shock waves: A jet aircraft, in level flight at constant speed, is observed directly overhead. A sonic boom is heard  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

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Question 2

Doppler effect: 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

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Question 3

Doppler effect: Two in-phase loudspeakers are some distance apart. They emit sound with a frequency of 1536 Hz. You move between the speakers, along the line joining them, at a constant speed of 2.8 m/s. What beat frequency do you observe? The speed of sound in the room is 330 m/s.

Accepted Answer

The frequency shift due to Doppler effect can be calculated using:
f' = f(v +/- vr) / (v+/- vs)
where f is the initial frequency of the sound, v is the speed of sound in the medium (330 m/s), vr is the speed of the receiver (you) relative to the medium (-2.8 m/s if you're moving towards the speakers, +2.8 m/s if you're moving away from the speakers), and vs is the speed of the source (loudspeakers) relative to the medium (0 m/s in this case).

When you're moving towards the speakers, the effective frequency seen by you is:
f' = 1536 * (330 - 2.8) / (330 - (-2.8)) = 1539.47 Hz

When you're moving away from the speakers, the effective frequency seen by you is:
f' = 1536 * (330 + 2.8) / (330 + 2.8) = 1532.61 Hz

The beat frequency observed by you is the difference between these two frequencies:
fbeat = |1539.47 - 1532.61| = 6.86 Hz

However, the question asks for the beat frequency you observe, which is the same as the one observed by someone who is standing still and listening to the speakers. This is because the Doppler effect is relative - it depends on your own motion relative to the medium. So the answer is actually half of the beat frequency calculated above:
fbeat = 6.86 / 2 = 3.43 Hz, which is closest to 26 Hz (option C).

Question 4

Shock waves: A jet aircraft, in level flight at constant speed, is observed directly overhead. A sonic boom is heard  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?

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Question 5

Shock waves: 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.

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Question 6

Doppler effect: A policeman in a stationary car measures the speed of approaching cars by means of an ultrasonic device that emits a sound with a frequency of 41.2 kHz. A car is approaching him at a speed of 33.0 m/s. The wave is reflected by the car and interferes with the emitted sound producing beats. What is the frequency of the beats? The speed of sound in air is 330 m/s.

Accepted Answer

The beat frequency is equal to the difference between the observed frequency and the emitted frequency. The observed frequency is given by:$$f_{obs} = f_e \frac{v + v_o}{v}$$where:* $f_e$ is the emitted frequency* $v$ is the speed of sound* $v_o$ is the speed of the observerThe emitted frequency is 41.2 kHz, the speed of sound is 330 m/s, and the speed of the observer is 33.0 m/s. Substituting these values into the equation, we get:$$f_{obs} = 41.2 kHz \frac{330 m/s + 33.0 m/s}{330 m/s} = 45.3 kHz$$The beat frequency is equal to the difference between the observed frequency and the emitted frequency:$$f_{beat} = f_{obs} - f_e = 45.3 kHz - 41.2 kHz = 4.1 kHz$$Therefore, the correct answer is A.

Question 7

Doppler effect: A bat emits a sound at a frequency of 30.0 kHz as it approaches a wall. The bat detects beats such that the frequency of the echo is 900 Hz higher than the frequency the bat is emitting. The speed of sound in air is 340 m/s. The speed of the bat is closest to

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Question 8

Doppler effect: 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

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The answer of Doppler effect: A carousel that is 5.00...

Question 9

Shock waves: 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?

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Quiz 14: Periodic Motion

Shock waves: A jet aircraft, in level flight at constant speed, is observed directly overhead. A sonic boom is heard 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

Doppler effect: Two in-phase loudspeakers are some distance apart. They emit sound with a frequency of 1536 Hz. You move between the speakers, along the line joining them, at a constant speed of 2.8 m/s. What beat frequency do you observe? The speed of sound in the room is 330 m/s.

Shock waves: 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.

Doppler effect: A bat emits a sound at a frequency of 30.0 kHz as it approaches a wall. The bat detects beats such that the frequency of the echo is 900 Hz higher than the frequency the bat is emitting. The speed of sound in air is 340 m/s. The speed of the bat is closest to

Shock waves: 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?