apparent change in wavelength of sound waves is 2.5cm when the source of sound is approaching stationary listener with velocity 8cm/s.Apparent decrease in the frequency of source when observer recedes from the same source at rest with a velocity of 30m/s is (velocity of sound =360 m/s)
how far is the sound travelled in the uhfdug
To find the apparent decrease in frequency, we can use the formula for the Doppler effect:
Δf/f = v/c
where Δf is the change in frequency, f is the frequency of the source, v is the relative velocity between the source and the observer, and c is the velocity of sound in the medium.
In the first scenario, the source of sound is approaching the stationary listener. Here, the change in wavelength (Δλ) is given as 2.5 cm, and the velocity of the source (v) is 8 cm/s.
We can find the frequency of the source (f) using the formula for the speed of waves:
v = fλ
where v is the velocity of the source, f is the frequency, and λ is the wavelength.
Substituting the given values, we can find the frequency of the source:
8 cm/s = f * λ
Since the change in wavelength (Δλ) is given as 2.5 cm, the initial wavelength (λ) is λ = Δλ + λ₀, where λ₀ is the wavelength of the source at rest.
λ = 2.5 cm + λ₀
Now we can substitute this value back into the equation:
8 cm/s = f * (2.5 cm + λ₀)
Simplifying the equation:
8 cm/s = 2.5f cm + f * λ₀
To find the value of λ₀, we need to know the velocity of sound (c). In the given information, the velocity of sound is given as 360 m/s.
Now, using the equation v = fλ, we can convert the velocity of sound from m/s to cm/s:
360 m/s * (100 cm/1 m) = f * λ₀
36000 cm/s = f * λ₀
Therefore, λ₀ = 36000 cm/s ÷ f.
Substituting the value of λ₀ back into the equation:
8 cm/s = 2.5f cm + f * (36000 cm/s ÷ f)
Simplifying further:
8 cm/s = 2.5f cm + 36000 cm/s
Now, rearrange the equation:
2.5f cm = 8 cm/s - 36000 cm/s
2.5f cm = -35992 cm/s
f = -35992 cm/s ÷ 2.5 cm
f ≈ -14397.6 s⁻¹
The negative frequency value indicates a decrease in frequency, which makes sense since the observer is receding from the source.
Finally, converting the frequency from s⁻¹ to Hz by taking the absolute value:
Δf = |f| ≈ |-14397.6 s⁻¹|
Apparent decrease in frequency ≈ 14397.6 Hz (approximately).