A stationary source emits sound waves of frequency $500\, Hz$. Two observers moving along a line passing through the source detect sound to be of frequencies $480\, Hz$ and $530\, Hz$. Their respective speeds are, in $m\,s^{-1}$ (Given speed of sound $= 300\, m/s$)
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A tuning fork resonates with a sonometer wire of length $1 \mathrm{~m}$ stretched with a tension of $6 \mathrm{~N}$. When the tension in the wire is changed to $54 \mathrm{~N}$, the same tuning fork produces $12$ beats per second with it. The frequency of the tuning fork is $\mathrm{Hz}$.
Two travelling waves ${y_1} = A\sin [k(x - c\,t)]$ and ${y_2} = A\sin [k(x + c\,t)]$ are superimposed on string. The distance between adjacent nodes is
What is minimum length of a tube, open at both ends, that resonates with tuning fork of frequency $350 Hz$ ? [velocity of sound in air $= 350 m/s$] ..... $cm$
A progressive wave travelling along the positive $x-$ direction is represented by $y(x, t) = A\,sin\,\left( {kx - \omega t + \phi } \right)$. Its snapshot at $t = 0$ is given in the figure For this wave, the phase $\phi $ is
Answer the following by appropriately matching the lists based on the information given in the paragraph.A musical instrument is made using four different metal strings, $1,2,3$ and $4$ with mass per unit length $\mu, 2 \mu, 3 \mu$ and $4 \mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range $L _0$ and $2 L _0$. It is found that in string$-1 \ (\mu)$ at free length $L _0$ and tension $T _0$ the fundamental mode frequency is $f _0$.
List $-I$ gives the above four strings while list $-II$ lists the magnitude of some quantity.
List $-I$
List $-II$
$(I)$ String $-1( \mu$ )
$(P) 1$
$(II)$ String $-2 (2 \mu)$
$(Q)$ $1 / 2$
$(III)$ String $-3 (3 \mu)$
$(R)$ $1 / \sqrt{2}$
$(IV)$ String $-4 (4 \mu)$
$(S)$ $1 / \sqrt{3}$
$(T)$ $3 / 16$
$(U)$ $1 / 16$
($1$) If the tension in each string is $T _0$, the correct match for the highest fundamental frequency in $f _0$ units will be,
$(1)$ $I \rightarrow P , II \rightarrow R , III \rightarrow S , IV \rightarrow Q$
$(2)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow T , IV \rightarrow S$
$(3)$ $I \rightarrow Q , II \rightarrow S , III \rightarrow R , IV \rightarrow P$
$(4)$ I $\rightarrow Q , II \rightarrow P , III \rightarrow R$, IV $\rightarrow T$
($2$) The length of the string $1,2,3$ and 4 are kept fixed at $L _0, \frac{3 L _0}{2}, \frac{5 L _0}{4}$ and $\frac{7 L _0}{4}$, respectively. Strings $1,2,3$ and 4 are vibrated at their $1^{\text {tt }}, 3^{\text {rd }}, 5^{\text {m }}$ and $14^{\star}$ harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of $T _0$ will be.
$(1)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow T , IV \rightarrow U$
$(2)$ $I \rightarrow T , II \rightarrow Q , III \rightarrow R$, IV $\rightarrow U$
$(3)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow R , IV \rightarrow T$
$(4)$ I $\rightarrow P , II \rightarrow R , III \rightarrow T , IV \rightarrow U$
A tuning fork gives $4$ beats with $50 cm$ length of a sonometer wire. If the length of the wire is shortened by $1 cm$, the number of beats is still the same. The frequency of the fork is
The pressure wave, $P = 0.01\,sin\,[1000t -3x]\,Nm^{-2},$ corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is $0\,^oC.$ On some other day when temperature is $T,$ the speed of sound produced by the same blade and at the same frequency is found to be $336 \,ms^{-1}$. Approximate value of $T$ is .... $^oC$