apparent change in wavelength of sound waves is 2.5cm when the source of sound is approaching stationary listener with velocity 8cm/s.
To calculate the apparent change in wavelength of sound waves, we can use the formula for the Doppler effect. The formula is given by:
Δλ = λ * (v / c)
Where:
- Δλ is the change in wavelength
- λ is the initial wavelength
- v is the velocity of the source of sound relative to the listener
- c is the speed of sound
We are given that the apparent change in wavelength is 2.5 cm (or 0.025 m) and the velocity of the source of sound is 8 cm/s (or 0.08 m/s). We also need to know the speed of sound, which is approximately 343 m/s at room temperature.
Let's plug in the values into the formula and solve for the initial wavelength (λ):
0.025 = λ * (0.08 / 343)
To isolate λ, we divide both sides of the equation by (0.08 / 343):
λ = 0.025 / (0.08 / 343)
Simplifying further:
λ = 0.025 * (343 / 0.08)
Calculating the equation:
λ ≈ 10.9844 m
Therefore, the initial wavelength of the sound waves is approximately 10.9844 meters.