Question

A certain sound has a frequency of 256 hertz and a wavelength of 1.3m.
(i) Calculate the speed of sound
(ii) What difference would be felt by a listener between the above sound and another sound travelling at the same speet, but of wavelength 2.6 m? ​

Answer 1

Given information to us:

• Frequency of sound = 256 hertz
• Wavelength of first sound = 1.3 m
• Wavelength of second sound = 2.6 m

Need to be solved:

• The speed of sound and difference felt by a listener between above and another sound.

Formula needed to be applied:

• Speed = Frequency × wavelength
• Frequency = Speed / wavelength

Step by step explaination:

Here we had been provided with the values of frequency (f) and wavelength it's symbol is λ.

We know this:

• The number of vibrations which had been made by the particle in one second is known as frequency (f)
• The distance which had been travelled by a wave in one time period of vibration is known of particle of a medium is known as wavelength (λ)

Thus the calculations for first sound is as follows:

⟹ Speed = Frequency × wavelength(λ)

⟹ Speed = 256 × 1.3

⟹ Speed = 256 × 13/10

⟹ Speed = 332.8 ms-¹

Now the calculations for second sound is as follows:

We already came to knew about the speed(V) that is 332.8 ms-¹.

Using the formula of frequency:

Frequency = Speed / wavelength

Substituting values:

⟹ Frequency = 332.8/2.6

⟹ Frequency = 332×10 / 2.6×10

⟹ Frequency = 128 Hz

Answer:

• Speed of first sound is 332.8 ms-¹
• And the difference felt by a listener between the above sound and another sound travelling at the same speed is 128 Hz.

Answer 2

$\Large\bf {\underline{ \underline{Given:-}}}$

• $: \implies$ Frequency = 256Hz
• $: \implies$ Wavelength = 1.3m

‎

$\Large\bf {\underline{ \underline{To \: Find:-}}}$

$: \implies$ Speed of the sound

$: \implies$ Difference felt between both sound

‎

$\Large\bf {\underline{ \underline{Step \: by \: step \: explaination:-}}}$

»» First of all we would calculate the value of speed that is by using the formula of speed that is : Speed = Frequency × wavelength. After that we would calculate the frequency that is: Speed / Wavelength. Always remember that frequency is always measured in hertz.

Lets solve it!!

Calculating the speed of sound by using the formula of speed (v) :

• $: \implies \: 256 \: \times \: 1.3$

Removing the decimal point we would get 10 as denominator:

• $: \implies \: 256 \: \times \: \dfrac{13}{10}$

Reducing to their lowest terms:

• $: \implies \: \cancel{256} \: \times \: \dfrac{13}{ \cancel{10} }$

• $: \implies \: 128 \: \times \: \dfrac{13}{5}$

Solving further:

• $: \implies \: \dfrac{1664}{5}$

• $: \implies \: \dfrac{ \cancel{1664}}{ \cancel{5}}$

• $: \implies \: 332.8$

Thus, speed of sound is 332.8 ms-¹ .

Here's the calculations for frequency by using the formula:

• $: \implies \: \dfrac{332.8}{2.6}$

Removing the decimal we get 10 in both denominator and numerator:

• $: \implies \: \dfrac{3328 \: \times \: 10}{26 \: \times \: 10}$

• $: \implies \: \dfrac{3328 \: \times \: \cancel{10}}{26 \: \times \: \cancel{10}}$

• $: \implies \: \dfrac{ \cancel{3328}}{ \cancel{26}}$

Thus frequency is 128 Hz

‎

$\Large\bf {\underline{ \underline{Conclusion:-}}}$

• (i) 332.8 ms-¹
• (ii) 128 Hertz