QuestionJune 15, 2025

6. A train is moving at 23m/s due east when it sounds a blast on its horn, frequency=164Hz What frequency is heard by the driver of a car moving due east at 15m/s along a road parallel to the tracks? Use 343m/s for the speed of sound Please show all work.(ref: p 410-417 v=343m/s vs=23m/s(train,east) vo=15m/s(car,east) fs=164Hz

6. A train is moving at 23m/s due east when it sounds a blast on its horn, frequency=164Hz What frequency is heard by the driver of a car moving due east at 15m/s along a road parallel to the tracks? Use 343m/s for the speed of sound Please show all work.(ref: p 410-417 v=343m/s vs=23m/s(train,east) vo=15m/s(car,east) fs=164Hz
6. A train is moving at 23m/s due east when it sounds a blast on its horn, frequency=164Hz What
frequency is heard by the driver of a car moving due east at 15m/s along a road parallel to the tracks?
Use 343m/s for the speed of sound Please show all work.(ref: p 410-417
v=343m/s
vs=23m/s(train,east)
vo=15m/s(car,east)
fs=164Hz

Solution
4.2(218 votes)

Answer

160.5 \, \text{Hz} Explanation 1. Identify the Doppler Effect Formula The formula for the observed frequency f_o when both source and observer are moving is: **f_o = f_s \frac{v + v_o}{v + v_s}**. 2. Substitute Given Values Substitute f_s = 164 \, \text{Hz}, v = 343 \, \text{m/s}, v_s = 23 \, \text{m/s}, and v_o = 15 \, \text{m/s} into the formula: f_o = 164 \times \frac{343 + 15}{343 + 23}. 3. Calculate the Observed Frequency Simplify and calculate: f_o = 164 \times \frac{358}{366}. 4. Perform the Division and Multiplication Calculate \frac{358}{366} \approx 0.9781, then multiply by 164: f_o \approx 160.5 \, \text{Hz}.

Explanation

1. Identify the Doppler Effect Formula<br /> The formula for the observed frequency $f_o$ when both source and observer are moving is: **$f_o = f_s \frac{v + v_o}{v + v_s}$**.<br /><br />2. Substitute Given Values<br /> Substitute $f_s = 164 \, \text{Hz}$, $v = 343 \, \text{m/s}$, $v_s = 23 \, \text{m/s}$, and $v_o = 15 \, \text{m/s}$ into the formula: <br /> $f_o = 164 \times \frac{343 + 15}{343 + 23}$.<br /><br />3. Calculate the Observed Frequency<br /> Simplify and calculate: $f_o = 164 \times \frac{358}{366}$.<br /><br />4. Perform the Division and Multiplication<br /> Calculate $\frac{358}{366} \approx 0.9781$, then multiply by $164$: $f_o \approx 160.5 \, \text{Hz}$.
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