Ige confused, the truck driver sound the horn of the truck, which has a frequency of 260HZ. The speed of sound in air is 340m/s. an observer hears the sound while traveling in a bus toward the truck at a speed of 30m/s.
a) what is the wavelength of the sound the whisle emits?
b)calculat the speed of sound relative to the observer on the bus when the truck is 1)approching the truck and 2)when the moving away from the truck.
c) calculate the frequency of the sound heard by the observer in b-1 and b-2.
a) wavelength = (sound speed)/(frequency) = 1.308 m
b1) 340+30 m/s = ___
b2) 340-30 m/s = ___
c1) Doppler-shifted frequency
= relative speed of sound/(wavelength)
= 370/1.308 = ___ Hz
c2) 310/1.308 = ___ Hz
To find the answers to these questions, we can use the formula for the doppler effect:
f' = (v + vr) / (v + vs) * f
where:
f' is the observed frequency
v is the speed of sound in air
vr is the velocity of the receiver (observer)
vs is the velocity of the source (truck)
f is the frequency emitted by the source (truck horn)
Let's solve each part step by step:
a) Wavelength of the Sound:
We can use the formula for wavelength:
wavelength (λ) = v / f
Given:
f = 260 Hz
v = 340 m/s
Substituting the values:
wavelength (λ) = 340 / 260
wavelength (λ) ≈ 1.31 m
So, the wavelength of the sound emitted by the truck horn is approximately 1.31 meters.
b) Speed of Sound Relative to the Observer on the Bus:
We can use the formula for relative velocity:
v' = v + vr
Given:
v = 340 m/s (speed of sound in air)
vr = 30 m/s (velocity of the observer on the bus)
For when the bus is approaching the truck:
v' = v + vr
v' = 340 + 30
v' = 370 m/s
For when the bus is moving away from the truck:
v' = v - vr
v' = 340 - 30
v' = 310 m/s
So, when the bus is approaching the truck, the speed of sound relative to the observer on the bus is 370 m/s. When the bus is moving away from the truck, the speed of sound relative to the observer on the bus is 310 m/s.
c) Frequency of the Sound Heard by the Observer:
We can use the formula for the observed frequency:
f' = (v + vr) / (v + vs) * f
Given:
f = 260 Hz
v = 340 m/s (speed of sound in air)
vr = 30 m/s (velocity of the observer on the bus)
For when the bus is approaching the truck (b-1):
f' = (v + vr) / (v + vs) * f
f' = (340 + 30) / (340 + 0) * 260
f' = 370 / 340 * 260
f' ≈ 283.5 Hz
For when the bus is moving away from the truck (b-2):
f' = (v + vr) / (v + vs) * f
f' = (340 + 30) / (340 - 0) * 260
f' = 370 / 340 * 260
f' ≈ 283.5 Hz
So, both when the bus is approaching and moving away from the truck, the frequency of the sound heard by the observer is approximately 283.5 Hz.