A man driving a car toward a large vertical wal sounds his horn. The car is traveling at 81 km/h. The echo off the wall is heard by the man at a frequency of 958 Hz. What is the frequency of the car's horn?
Vc = 81000m/3600s = 22.5 m/s. = Velocity
of car.
F = ((V+Vr)/(V+Vc)))*Fh = 958Hz.
((345+22.5)/(343-22.5))*Fh = 958
367.5Fh/322.5 = 958
1.140Fh = 958
Fh = 841 Hz. = Freq. of horn.
To find the frequency of the car's horn, we can use the Doppler effect formula:
f' = f ((v + v_0) / (v - v_s))
Where:
f' is the observed frequency
f is the source frequency
v is the speed of sound
v_0 is the velocity of the observer
v_s is the velocity of the source
Let's break down the given information and plug it into the formula:
- The observed frequency (f') is 958 Hz.
- The speed of sound (v) is a constant and can be assumed as 343 m/s.
- The velocity of the observer (v_0) is 0 m/s since the man is stationary.
- The velocity of the source (v_s) can be calculated using the following formula:
v_s = v + v_0
Now, let's calculate v_s:
v_s = 343 m/s + 0 m/s
v_s = 343 m/s
Now we can calculate the source frequency (f) using the formula:
f = f' * (v - v_s) / (v + v_0)
Substituting the values:
f = 958 Hz * (343 m/s - 343 m/s) / (343 m/s + 0 m/s)
f = 958 Hz
Therefore, the frequency of the car's horn is 958 Hz.
To find the frequency of the car's horn, we need to understand the principle of the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave.
1. Let's denote the actual frequency of the car's horn as f (in Hz).
2. The man hears the echo of the horn, which has a frequency of 958 Hz.
3. When the sound wave from the car's horn travels towards the wall, it experiences a frequency shift due to the car's motion.
4. Since the car is moving toward the wall, the observed frequency of the horn will be higher than the actual frequency.
This is known as a positive Doppler effect.
Mathematically, the observed frequency (f') can be calculated using the formula:
f' = f * (v + v₀) / (v + vₛ)
where:
- f' is the observed frequency
- f is the actual frequency of the car's horn
- v is the speed of sound in air (approximately 343 m/s)
- v₀ is the speed of the car (81 km/h)
- vₛ is the speed of sound reflected back from the wall (same as v)
Now, let's calculate the frequency of the car's horn using this formula.
1. Convert the speed of the car from km/h to m/s:
v₀ = 81 km/h * (1000 m/1 km) / (3600 s/1 h) = 22.5 m/s
2. Substitute the given values into the formula:
f' = f * (343 m/s + 22.5 m/s) / (343 m/s + 343 m/s)
3. Simplify the formula:
f' = f * (365.5 m/s) / (686 m/s)
f' = f * 0.5338
4. Solve for f by dividing both sides of the equation by 0.5338:
f = f' / 0.5338
5. Substitute the observed frequency:
f = 958 Hz / 0.5338
6. Calculate the frequency:
f ≈ 1797 Hz
Therefore, the frequency of the car's horn is approximately 1797 Hz.