Question

1. a wave has a frequency of 540 hz and is traveling at 340 m/s. what is its wavelength?
2. a wave has a wavelength of 125 meters is moving at a speed of 20 m/s. what is its frequency?
3. a wave has a frequency of 900 hz and a wavelength of 200 m. at what speed is this wave traveling?

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave is \(v = f\lambda\), where \(v\) is the speed of the wave, \(f\) is the frequency, and \(\lambda\) is the wavelength. We can re - arrange the formula to solve for the unknown variable.

For problem 6:

Step2: Solve for wavelength \(\lambda\)

Given \(v = 340\ m/s\) and \(f=540\ Hz\). From \(v = f\lambda\), we can get \(\lambda=\frac{v}{f}\).
Substitute the values: \(\lambda=\frac{340}{540}\approx0.63\ m\)

For problem 7:

Step2: Solve for frequency \(f\)

Given \(v = 20\ m/s\) and \(\lambda = 125\ m\). From \(v = f\lambda\), we can get \(f=\frac{v}{\lambda}\).
Substitute the values: \(f=\frac{20}{125}=0.16\ Hz\)

For problem 8:

Step2: Solve for speed \(v\)

Given \(f = 900\ Hz\) and \(\lambda=200\ m\). Using the formula \(v = f\lambda\).
Substitute the values: \(v=900\times200 = 180000\ m/s\)

Answer:

1. The wavelength is approximately \(0.63\ m\).
2. The frequency is \(0.16\ Hz\).
3. The speed of the wave is \(180000\ m/s\).