In this post, we will solve a set of **Wave Equation Numericals** using the wave equation itself.

## Wave Equation Numericals – solved

Here, we will go through the equation that is used to solve the numerical problems given in this post. Then we will solve the wave equation numericals one by one.

**Wave Equation Numericals formula used**

This equation that is used to solve the numerical problems in this post is called Wave Equation.

Wave equation:

v = f λwhere v = speed of the wave, f = frequency of the wave, and λ is the wavelength of the wave.

**Numericals on Wave Equation – Questions and Solution**

1] What is the frequency of a longitudinal wave that has a wavelength of 2.0 m and a speed of 340 m s^{−1}?

**Solution**:

The wave equation states that v = f λ

f = v/λ

=>f =340/2 Hz

Frequency = 170 Hz

2] What is the frequency of a transverse wave that has a wavelength of 4.0 × 10^{−7}m and a speed of 3.0 × 10^{8}m s^{−1}?

**Solution:**

As per the wave equation v = f λ

f = v/λ

=>f =[3.0 × 10]/[^{8}4.0 × 10] Hz^{−7}

Frequency = 0.75 x 10^{15}Hz

3] Calculate the period of a longitudinal wave that has a wavelength of 2.0 m and a speed of 340 m s

^{−1}.

**Solution:**

As per the wave equation v = f λ

=>f = v/λ

As, period T = 1/f

hence, T = 1/ [v/λ]

=> T = λ/v

Hence, the period of a longitudinal wave T = λ/v = 2/340 sec = 5.9 × 10

^{−3}s

4 ] Calculate the period of a transverse wave that has a wavelength of 4.0 × 10

^{−7}m and a speed of 3.0 × 10^{8}m s−1.

**Solution:**

As per the wave equation v = f λ

=>f = v/λ

As, period T = 1/f

hence, T = 1/ [v/λ]

=> T = λ/v

Hence, the period of a longitudinal wave T = λ/v = [4.0 × 10

^{−7}]/[3.0 × 10^{8}] sec = 1.33 × 10^{−15}s