Question

Physics !!

Chapter :- Wave Motion and Sound.

Kindly solve it with a proper explanation :)

#No spams !!​

Answer 1

Hi,

As we know for the vibration in n nodes,

$I \: = \: \frac{(n - 1)λ}{2} ...1$

While given the fundamental frequency to be f = 25 hz

So 25 = $\frac{v}{2I}$

So velocity of the wave in string = 50I = 50 × 3 = 150 m / s

When it is made to vibrate in 7 nodes

$I \: = \: \frac{6λ}{2} (from \: 1)$

So λ = $\frac{21}{6} = \frac{6}{6} = 1m$

Hence the frequency f = $\frac{v}{λ}$ or f = $\frac{150}{1} = 150Hz$☑

Now when the string is made to vibrate in the 4th harmonic

f = 4 ( Fundamental Frequency ) = 4 × 25 = 100 Hz ☑

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\red{Answer\:=\:100\:Hz\:and\:150\:Hz}}}}$

Answer 2

$\sf{\underline{\boxed{\large{\blue{\mathsf{Solution}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• vibration of a stretched string Frequency = 25Hz
• length = 3m

_______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• frequency of vibration when vibrated with 7 nodes = ???
• frequency of 4th harmonic = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{frequency = \dfrac{v}{2l}}}}}$

⠀⠀

: $\sf\implies \: {\bold { 25 = \dfrac{V} { 2\times 3 } }}$

: $\sf\implies \: {\bold { 25 = \dfrac{V} { 6 } }}$

⠀⠀⠀⠀

: $\sf\implies \: {\bold{ V = 25 \times 6 }}$

⠀⠀

: $\sf\implies \: {\bold{ V = 150m/s }}$

⠀⠀⠀⠀

$\sf{\pink{\boxed{\bold{V = 150 m/s }}}}$

⠀⠀

$\sf{\red{\boxed{\bold{l = \dfrac{ ( n - 1 )\lambda}{ 2 } }}}}$

⠀⠀⠀⠀

: $\sf\implies \: {\bold { l = \dfrac{( 7 -1 )\lambda } { 2 } }}$

⠀⠀

: $\sf\implies \: {\bold { 3 = \dfrac{( 6 )\lambda } { 2 } }}$

⠀⠀⠀⠀

: $\sf\implies \: {\bold {3 \times 2 = 6 \lambda}}$

⠀⠀⠀⠀

:$\sf\implies \: {\bold { \lambda = \dfrac{6}{6}}}$

⠀⠀⠀⠀

: $\sf\implies \: {\bold{\lambda = 1m }}$

⠀⠀⠀⠀

$\sf{\pink{\boxed{\bold{\lambda = 1m }}}}$

⠀⠀

$\sf{\red{\boxed{\bold{frequency = \dfrac{v}{\lambda}}}}}$

⠀⠀⠀⠀

$\sf\longrightarrow{\bold{ frequency = \dfrac{150}{1}}}$

⠀⠀

$\sf\longrightarrow {\bold { frequency = 150Hz }}$

⠀⠀

$\sf{\orange{\boxed{\bold{ frequency = 150 Hz}}}}$

• frequency of 4th harmonic

⠀⠀

frequency of 4th harmonic = 4 x f

⠀⠀

frequency of 4th harmonic = 4 x 25

⠀⠀⠀⠀

frequency of 4th harmonic = 100 Hz

⠀⠀

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• frequency of vibration when vibrated with 7 nodes is 150 Hz
• frequency of 4th harmonic is 100Hz.