A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 120 rpm. Assume the room temperature is 20 degrees Celsius.

Part A: What is the highest frequency heard by a student in the classroom? (in Hz)

Part B: What is the lowest frequency heard by a student in the classroom? (in Hz)

(a) f = 622.79 Hz

(b) f = 578.82 Hz

Explanation:

Given Data

Frequency = 600 Hz

Distance=1.0 m

n=120 rpm

Temperature = 20 degree

Before solve this problem we need to find The sound generator moves on a circular with tangential velocity

So

Speed of sound is given by

c = √ (γ·R·T/M) ... in an ideal gas

where γ heat capacity ratio

R universal gas constant

T absolute temperature

M molar mass

The speed of sound at 20°C is

c = √ (1.40 * 8.314472J/molK * 293.15K / 0.0289645kg/mol)

c = 343.24m/s

The sound moves on a circular with tangential velocity

vt = ω·r ... where ω=2·π·n

vt = 2·π·n·r

vt = 2·π · 120min⁻¹ · 1m

vt = 753.6 m/min

convert m/min to m/sec

vt = 12.56 m/s

Part A

For maximum frequency is observed

v = vt

f = f₀ / (1 - vt/c)

f = 600Hz / (1 - (12.56m/s / 343.24m/s))

f = 622.789 Hz

Part B

For minimum frequency is observed

v = - vt

f = f₀ / (1 + vt/c)

f = 600Hz / (1 + (12.56m/s / 343.24m/s))

f = 578.82 Hz