A transverse wave 1.1cm in amplitude is propagating on a string; the wave frequency is 44 Hz. The string is under 23-N tension and has mass per unit length of 16g/m . What is the wave speed?
What I've done:
using sqrt(Tension/mass_per_unit):
sqrt(23/16)=1.19m/s
But not sure how to incorporate amplitude and frequency?
Any help appreciated!
mass is grams, so 0.016 .. pop that in your formula and you're golden
To find the wave speed, you can use the formula:
v = f λ
where v is the wave speed, f is the frequency, and λ is the wavelength.
Since the given wave is a transverse wave on a string, the amplitude (A) is not a direct factor in determining the wave speed. The amplitude only affects the maximum displacement of the wave from its equilibrium position.
To find the wavelength (λ), you can use the formula:
λ = 2A
where A is the amplitude. In this case, A is given as 1.1 cm, which is equal to 0.011 m.
So, λ = 2 * 0.011 = 0.022 m
Now, you have the values for frequency (f = 44 Hz) and wavelength (λ = 0.022 m). Substituting these values into the wave speed formula, you get:
v = 44 * 0.022 = 0.968 m/s
Therefore, the wave speed is approximately 0.968 m/s.