DOPPLER EFFECT II: FREQUENCIES

If a listener L is at rest and the siren in Example 16.14 is moving away from L at 30 m/s, what frequency does the listener hear?

Question

DOPPLER EFFECT II: FREQUENCIES

If a listener L is at rest and the siren in Example 16.14 is moving away from L at 30 m/s, what frequency does the listener hear?

Accepted Answer

IDENTIFY and SET UP:

Our target variable is the frequency [latex]f_L[/latex] heard by a listener behind the moving source. Figure 16.31 shows the situation. We have [latex]v_L[/latex] = 0 and [latex]v_S[/latex] = +30 m/s (positive, since the velocity of the source is in the direction from listener to source).

EXECUTE:

From Eq. (16.29) ([latex]f_{\mathrm{L}}=\frac{v+v_{\mathrm{L}}}{v+v_{\mathrm{S}}} f_{\mathrm{S}}[/latex]),

[latex]f_{\mathrm{L}}=\frac{v}{v+v_{\mathrm{S}}} f_{\mathrm{S}}=\frac{340 \mathrm{~m} / \mathrm{s}}{340 \mathrm{~m} / \mathrm{s}+30 \mathrm{~m} / \mathrm{s}}(300 \mathrm{~Hz})=276 \mathrm{~Hz}[/latex]

wavelength behind the source (where the listener in Fig. 16.31 is located) is 1.23 m. The wave speed relative to the stationary listener is v = 340 m/s even though the source is moving, so

[latex]f_{\mathrm{L}}=\frac{v}{\lambda}=\frac{340 \mathrm{~m} / \mathrm{s}}{1.23 \mathrm{~m}}=276 \mathrm{~Hz}[/latex]

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