Question

In air, a sound wave with a frequency of 196 hz has a wavelength of about 1.76 meters. what is the wavelength of a wave if the frequency is increased to 784 hz?

Answer 1

The wavelength of the sound wave if the frequency is increased to the given value is 0.44m.

Given the data in the question;

• Frequency of sound wave a; $f_a = 196Hz = 196s^{-1}$

• Wavelength of sound wave a; $\lambda _a = 1.76m$

Speed of sound wave; $v =\ ?$

• Frequency of sound wave b; $f_b = 784Hz = 784s^{-1}$

Wavelength of sound wave b; $\lambda _b = ?$

Wavelength

Wavelength is simply the distance over which the shapes of waves are repeated. It is the spatial period of a periodic wave.

It is expressed as;

$\lambda = \frac{v}{f}$

Where v is velocity and f is frequency.

First, we calculate the velocity of the sound wave in air from sound wave a.

$\lambda = \frac{v}{f}\\ \\1.76m= \frac{v}{196s^{-1}}\\\\v = 1.76m * 196s^{-1}\\\\v = 344.96m/s$

Now, we determine the wavelength of sound wave b using the velocity of sound wave in air calculated above.

$\lambda = \frac{v}{f}\\ \\\lambda = \frac{344.96m/s}{784s^{-1}}\\\\\lambda = 0.44m$

Therefore, the wavelength of the sound wave if the frequency is increased to the given value is 0.44m.

Learn more about wavelength: brainly.com/question/27120701