Question

HELP ;

A wave is traveling at a constant speed. The frequency is 2 Hertz, and the wavelength is 1 meter. How would the wave properties change if the wavelength decreased from 1 to
0.5 while the speed stayed the same?
The amplitude would double.

The amplitude would decrease by one half.

The frequency would double.

The frequency would decrease by one half.

Answer 1

The answer is C The frequency would double.

Step-by-step explanation:

Answer 2

The frequency would double.

Step-by-step explanation:

Given:

Speed of wave (v) = constant.

Frequency of wave initially (f₁) = 2 Hz

Initial wavelength of the wave (λ₁) = 1 m

Final wavelength of the wave (λ₂) = 0.5 m

Final frequency of the wave (f₂) = ?

We know that the product of wavelength and frequency of the wave is equal to the speed of the wave.

Therefore, framing in equation form, we have:

Wavelength × Frequency = Speed

`\lambda* f=v`

It is given that speed of the wave remains the same. So, the product must always be a constant.

Therefore,

`\lambda* f=constant\ or\ \\\lambda_1* f_1=\lambda_2* f_2`

Now, plug in the given values and solve for 'f₂'. This gives,

`1* 2=0.5* f_2\\\\f_2=(2)/(0.5)=4\ Hz`

Therefore, the final frequency is 4 Hz which is double of the initial frequency.

f₂ = 2f₁ = 2 × 2 = 4 Hz

So, the second option is correct.