a speaker at a concert generates 1 x 10^-2 w/m^2 at a distance of 20m form the speaker at a frequency of 1kHz
1) calculate the wavelength of the waves emitted.
b) what is the intensity level at 20m
To calculate the wavelength of the waves emitted by the speaker, you can use the formula:
wavelength (λ) = speed of sound (v) / frequency (f)
The speed of sound in air is approximately 343 meters per second. The frequency given is 1kHz, which is equivalent to 1000 Hz.
a) Calculating the wavelength:
λ = 343 m/s / 1000 Hz
λ = 0.343 m
Therefore, the wavelength of the waves emitted by the speaker is approximately 0.343 meters.
b) To calculate the intensity level at 20m, you need to use the formula for sound intensity level (IL):
IL = 10 * log10(I / I0)
Where:
IL is the sound intensity level in decibels (dB),
I is the sound intensity in watts per square meter (W/m^2),
I0 is the reference sound intensity, which is the threshold of human hearing and is approximately 1 x 10^-12 W/m^2.
In this case, the sound intensity given is 1 x 10^-2 W/m^2.
IL = 10 * log10(1 x 10^-2 / 1 x 10^-12)
IL = 10 * log10(1 x 10^10)
IL = 10 * 10
IL = 100 dB
Therefore, the intensity level at 20m from the speaker is 100 decibels.