(B) The resonant frequencies of a string fixed at both ends are given by $f_n = n \cdot f_0$,where $f_0$ is the fundamental frequency and $n$ is an in

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(B) The resonant frequencies of a string fixed at both ends are given by $f_n = n \cdot f_0$,where $f_0$ is the fundamental frequency and $n$ is an integer $(n = 1, 2, 3, \dots)$.Given two consecutive resonant frequencies $f_n = 315\,Hz$ and $f_{n+1} = 420\,Hz$.The difference between two consecutive resonant frequencies is the fundamental frequency $f_0$.$f_0 = f_{n+1} - f_n = 420\,Hz - 315\,Hz = 105\,Hz$.Thus,the lowest resonant frequency (fundamental frequency) is $105\,Hz$.

Class 11 Physics Waves and Sound Transverse Stationary Waves and Sonometer

Medium

$A$ string is stretched between two fixed points separated by $75\,cm$. It is observed to have resonant frequencies of $420\,Hz$ and $315\,Hz$. There are no other resonant frequencies between these two. Then,the lowest resonant frequency for this string is ..... $Hz$.

A
$10.5$
B
$105$
C
$1.05$
D
$1050$

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Waves and Sound

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Transverse Stationary Waves and Sonometer

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$A$ tuning fork is sounded with a sonometer wire of length $95 \, cm$ or $100 \, cm$,producing $4$ beats per second in both cases. What is the frequency of the tuning fork in $Hz$?

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$A$ string is stretched between two fixed points separated by $75\,cm$. It is observed to have resonant frequencies of $420\,Hz$ and $315\,Hz$. There are no other resonant frequencies between these two. Then,the lowest resonant frequency for this string is ..... $Hz$.

Similar Questions

$A$ violin emits sound waves of frequency $n_1$ under tension $T$. When tension is increased by $44\%$,keeping the length and mass per unit length constant,the frequency of sound waves becomes $n_2$. The ratio of frequency $n_2$ to frequency $n_1$ is:

$A$ sonometer wire of length $114\, cm$ is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1 : 3 : 4$?

The fundamental frequency of a sonometer wire is $50 \text{ Hz}$ for a given length and tension. If the length is increased by $25\%$ while keeping the tension constant, what is the percentage change in the frequency of the second harmonic?

$L$ length and $M$ mass uniform wire is stretched between two fixed points with tension $F$. $A$ sound of frequency $\mu$ is impressed on it. The maximum vibrational energy exists in the wire when $\mu$ =

$A$ tuning fork is sounded with a sonometer wire of length $95 \, cm$ or $100 \, cm$,producing $4$ beats per second in both cases. What is the frequency of the tuning fork in $Hz$?

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