Question

A sound wave travels at a speed of 339 m/s. If its wavelength is 1.5 cm, what is the frequency of the wave? Will it be audible?​

Answer 1

Answer:

A sound wave travels at a speed of 339 m s –1 . If its wavelength is 1.5 cm, what is the frequency of the wave? Will it be audible? Frequency of sound is 22,600 Hz.

Answer 2

Provided Information:

• Velocity of the sound $(\nu)$ = 339 m/s

• Wave length $(\lambda)$ = 1.5 cm

To calculate:

• Frequency $(f )$

Conversion of units:

Let's first convert the units of wave length $(\lambda)$ in its standard form.

$\sf{ \longrightarrow \: 1 \: m = 100 \: cm} \\ \\ \sf{ \longrightarrow \: 1 \: cm = \dfrac{ 1 }{100} \: m} \\ \\ \sf{ \longrightarrow \: 1.5 \: cm = \dfrac{ 1.5 }{100} \: m} \\ \\ \sf{ \longrightarrow \: 1.5 \: cm = \dfrac{ 15 }{1000} \: m} \\ \\ \longrightarrow\underline{\boxed{\sf{1.5 \: cm = 0.015 \: m}}} \: \red{\bigstar}$

Calculating frequency:

$\star \: \underline{ \boxed{ \sf \pink{ \: \nu = \it{f} \times \lambda}}} \\ \\ \bull \: f = frequency \\ \bull \: \nu = velocity⠀⠀⠀⠀ \\ \bull \: \lambda = wavelength \\ \\ \sf{ \longrightarrow \: 339 = \it{f} \times \sf{0.015}} \\ \\ \\ \sf{ \longrightarrow \: \it{f} = \sf{ \dfrac{339}{0.015} \: Hz}} \\ \\ \\ \longrightarrow\it{f} = \sf{ \dfrac{339000}{15} \: Hz} \\ \\ \\ \longrightarrow \: \underline{\boxed{\sf{\it{f} = \sf{ 22600 \: Hz} }}} \: \red{\bigstar}$

Henceforth, frequency is 22600 Hz.

→ No, it won't be audible because it is untrasonic sound i.e , it has frequency above 20000 Hz & humans can't hear frequency above 20000 Hz.

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More Information:

• Wavelength is the distance in which sound repeats itself.
• SI unit of wavelength is metre (m).
• Frequency is equivalent to number of waves made by body in one second.
• SI unit of frequency is Hertz (Hz).
• Velocity of wave means distance travelled by it in one second.
• SI unit of velocity is m/s.