Question

A source is emitting waves of frequency 400Hz and wave-length 0.3m. Then how long does the wave takes to travel 300m?​

Answer 1

Given:-

• Frequency ,f = 400 Hz
• Wave length , λ = 0.3m

To Find:-

• Time taken to wave to travel,d 300 m

Solution:-

⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

We know that wave speed (v) is the product of wave length & frequency .

• v = f λ

where,

• v denote wave speed
• f denote frequency
• λ denote wavelength

Substitute the value we get

$:\implies$ v = 400×0.3

$:\implies$ v = 40×3

$:\implies$ v = 120 m/s

• So , the wave speed is 120m/s

Ww have to calculate the time taken by wave to travels 300m .

• t = d/v

where,

• v denote wave speed
• d denote distance
• t denote time taken

Substitute the value we get

$:\implies$ t = 300/120

$:\implies$ t = 2.5 s

• Hence, the time taken to travel 300m is 2.5 second.

Answer 2

$\huge{\underline{{\purple{Given :}}}}$

• A source is emitting waves of frequency 400 Hz and wavelength 0.3 m.

$\huge{\underline{{\purple{To\:Find :}}}}$

• Time will it take to travel 300 m

$\huge{\underline{{\purple{Formula\:Used :}}}}$

• ${\boxed{\bf{\red{v =nλ}}}}$

• ${\boxed{\bf{\red{Speed(v) =\dfrac{Distance(d)}{Time(t)}}}}}$

$\huge{\underline{{\purple{Solution :}}}}$

${\underline{\bf{\red{Using,\:v =nλ}}}}$

${\underline{\bf{\purple{Here,}}}}$

• ${\bf{\red{n = 400 Hz}}}$

• ${\bf{\red{λ = 0.3 m}}}$

${\underline{\bf{\purple{Putting\:Values,}}}}$

${\sf{\red{:\implies\:v =400\times0.3}}}$

${\bf{\red{:\implies\:v =120ms^{-1}}}}$

${\underline{\bf{\purple{Now,}}}}$

${\sf{\red{:\implies\: t=\dfrac{d}{v}}}}$

${\sf{\red{:\implies\: t=\dfrac{300}{120}}}}$

${\sf{\red{:\implies\: t=\dfrac{30}{12}}}}$

${\sf{\red{:\implies\: t=\dfrac{5}{2}}}}$

${\boxed{\bf{\red{:\implies\: t=2.5\:sec}}}}$

Hence, it will take 2.5sec the wave to travel 300m.

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