PhysicsLAB: Doppler Effect: Source Moving

Refer to the following information for the next three questions.

Part I. Three observers are standing around a stationary “speaker” which acts like a point source for a sound wave.

The speed of sound for the waves produced by the “speaker” is 350 m/s.

Do each of the listeners hear the same frequency of sound? Explain.

By measuring the distance between waves crests (to the nearest 0.1 cm), what is the wavelength produced by the “speaker”? (let, 1 cm = 1 meter)

Remembering that v_w = f λ, what frequency would the listeners hear in hertz?

Refer to the following information for the next four questions.

Part II. In the next diagram, the source is travelling towards the right through the same medium as above. (v_w = 350 m/sec)

By measuring the distance between waves crests (to the nearest 0.1 cm) along the line between the source and the observer, what wavelength reaches each listener? (once again, let 1 cm = 1 meter) What apparent frequency does each one hear?

listener

wavelength
(m)

frequency
(hz)

The actual wavelength can be determined by comparing the two diametrically opposed listeners along the direction of the source's motion (in our case, #1 and #4).

The apparent wavelength "heard" by listener #1 can be stated with the equation

λ₁ = λ_actual + Δλ

while the apparent wavelength "heard" by listener #4 can be state with the equation

λ₄ = λ_actual - Δλ

remembering that the Δ means the difference (in this case the apparent wavelength and the actual).

Adding these two simultaneous equations yields the equation

λ₁ + λ₄= 2λ_actual

Refer to the following information for the next three questions.

Using the equations shown above and the data from Part II, calculate the requested values.

Determine the actual wavelength of the source

Using the wave speed (350 m/s) and the wave equation, determine the actual frequency of the source.

Using the relationship Δλ / λ_actual = v_source / v_wave, determine the speed of the source in m/sec.

Refer to the following information for the next four questions.

Part III. The “speaker” now begins to play a new frequency while moving to the left.

By measuring the distance between waves crests (along the line between the source and the observer), what wavelength reaches each listener? (once again, let 1 cm = 1 meter) What apparent frequency does each one hear?

listener

wavelength
(m)

frequency
(hz)

The wavelengths and frequencies in the previous section (Part III) are the apparent values measured by the listeners (1‐4). The actual wavelength, frequency and the speed of the source can be determined once again by comparing the two diametrically opposed listeners along the direction of the source's motion (in our case, #1 and #4).

Calculate the actual wavelength of the source in meters.

Using the wave speed (350 m/s) and the wave equation, calculate the actual frequency of the source in hertz.

Using the relationship Δλ / λ_actual = v_source / v_wave, determine the speed of the source in m/sec.

Refer to the following information for the next four questions.

Conclusions

Does the direction of the “source’s” motion affect the actual frequency of the “source”?

yesno

Why do we not speak about an "apparent velocity" of a moving source?

In each case, the location of listener #2 is at right angles to direction of the source's velocity, how does the frequency he hears compare to the actual frequency of the source?

How does the location of a listener affect the frequency heard?