Question

A transverse wave of wavelength 40cm travels in air at a frequency 2500Hz. Calculate the time taken by this wave to travel a distance of 4km.

(If possible please answer quickly)

Answer 1

Topic :- Waves

Given :- A transverse wave of wavelength 40 cm travels in air at a frequency 2500 Hz.

To Find :- The time taken by this wave to travel a distance of 4 km.

Formula Used :-

v = f.λ

where

v = Speed of wave

f = Frequency of wave

λ = Wavelength of wave

Solution :-

It is given that :-

f = 2500 Hz

λ = 40 cm or 0.4 metre

Applying formula,

v = f.λ

v = 2500 × 0.4 m/s

v = 1000 m/s or

v = 1 km/s

Speed of wave is 1 km/s.

Now,

It is given that,

Distance = 4 km

Speed = 1 km/s ....( calculated above )

Speed = Distance / Time

Time = Distance / Speed

Applying formula,

Time = 4 km / 1 km/s

Time = 4 seconds

Answer :-

So, the time taken by this wave to travel a distance of 4 km is 4 seconds.

Answer 2

${\blue{\underline{\underline{\sf{Given\: :}}}}}$

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• Wavelength = λ = 40cm = 0.4m
• Frequency = f = 2500 Hz

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${\blue{\underline{\underline{\sf{To \: Find \: :}}}}}$

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• Time taken by wave to travel 4km = ??

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${\blue{\underline{\underline{\sf{Solution\: :}}}}}$

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From relation ;

$\star \: {\purple{\boxed{\frak{Velocity ( V) = Wavelength (\lambda) \times Frequency (f) }}}}$

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:⇒ Velocity = 0.4m × 2500 Hz

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:⇒Velocity = 1000 m/s

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• Now ; since the wave is same in both the cases , so Velocity will also be same

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Therefore ;

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:⇒ 1000 = 4000m × f

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:⇒ f = 1000 / 4000

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:⇒f = 1 / 4

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$: \implies \: {\pink{\boxed{\frak{ f = \dfrac{1}{4}}}}}\star$

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Now ; from relation :

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$\star \: {\purple{\boxed{\frak{Time\: period = \dfrac{1}{frequency}}}}}$

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$\sf : \implies { Time \: taken = \dfrac{1}{\dfrac{1}{4}}}$

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$\sf : \implies { Time \: taken = 1 \times 4 }$

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$\sf : \implies { Time \: taken = 4 seconds }$

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$: \implies \: {\pink{\boxed{\frak{ Time = 4 \: seconds }}}}\star$