DOPPLER EFFECT III: A MOVING LISTENER
If the siren is at rest and the listener is moving away from it at 30 m/s, what frequency does the listener hear?
Question 16.16: DOPPLER EFFECT III: A MOVING LISTENER If the siren is at res...
IDENTIFY and SET UP:
Again our target variable is f_L, but now L is in motion and S is at rest. Figure 16.32 shows the situation. The velocity of the listener is v_L = -30 m/s (negative, since the motion is in the direction from source to listener).
EXECUTE:
From Eq. (16.29) (f_{\mathrm{L}}=\frac{v+v_{\mathrm{L}}}{v+v_{\mathrm{S}}} f_{\mathrm{S}}),
f_{\mathrm{L}}=\frac{v+v_{\mathrm{L}}}{v} f_{\mathrm{S}}=\frac{340 \mathrm{~m} / \mathrm{s}+(-30 \mathrm{~m} / \mathrm{s})}{340 \mathrm{~m} / \mathrm{s}}(300 \mathrm{~Hz})=274 \mathrm{~Hz}
EVALUATE: Again the source and listener are moving apart, so f_L < f_S. Note that the relative velocity of source and listener is the same as in Example 16.15, but the Doppler shift is different because v_S and v_L are different.
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