Question

A transverse wave propagates along a stretched string with a velocity of 15 m/s. The amplitude of the wave is 0.25 m and the wavelength is 2.5 m. Determine the frequency, period, and angular frequency of the wave.

Answer

To find the frequency (f), period (T), and angular frequency (ω) of the wave, we can use the following formulas:

1. Frequency (f) = wave speed (v) / wavelength (λ)
2. Period (T) = 1 / frequency (f)
3. Angular frequency (ω) = 2π * frequency (f)

Given information:

• Wave speed (v) = 15 m/s
• Amplitude (A) = 0.25 m
• Wavelength (λ) = 2.5 m

First, let's calculate the frequency (f):

f = v / λ

Substituting the given values:

f = 15 m/s / 2.5 m

f ≈ 6 Hz

Next, let's calculate the period (T):

T = 1 / f

Substituting the calculated frequency:

T = 1 / 6 Hz

T ≈ 0.1667 s

Finally, let's calculate the angular frequency (ω):

ω = 2π * f

Substituting the calculated frequency:

ω = 2π * 6 Hz

ω ≈ 37.7 rad/s

Therefore, the frequency of the wave is approximately 6 Hz, the period is approximately 0.1667 s, and the angular frequency is approximately 37.7 rad/s.