Answer to Question #201503 in Physics for yoo

Question

The frequency of a car horn is 400 Hz. Find (a) the wavelength of the sound, and (b) the frequency observed if the car moves with a speed us = 34.0 m/s through still air toward a stationary receiver. Take the speed of sound in air to be 340 m/s. (c) Find the frequency observed if the car is stationary and a receiver moves with a speed us= 34.0 m/s toward the car.

Answer 1

(a)

$$\lambda=\dfrac{v}{f}=\dfrac{340\ \dfrac{m}{s}}{400\ Hz}=0.85\ m.$$

(b)

$$f_o=f_s(\dfrac{v}{v-v_s})=400\ Hz\cdot\dfrac{340\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-34\ \dfrac{m}{s}}=444\ Hz.$$

(c)

$$f_o=f_s(\dfrac{v+v_o}{v})=400\ Hz\cdot\dfrac{340\ \dfrac{m}{s}+34\ \dfrac{m}{s}}{340\ \dfrac{m}{s}}=440\ Hz.$$