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A vibrating string of certain length $\ell$ under a tension $\mathrm{T}$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75 \mathrm{~cm}$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $\mathrm{n}$. Now when the tension of the string is slightly increased the number of beats reduces $2$ per second. Assuming the velocity of sound in air to be $340 \mathrm{~m} / \mathrm{s}$, the frequency $\mathrm{n}$ of the tuning fork in $\mathrm{Hz}$ is
A sinusoidal wave of frequency $500 \,Hz$ has a speed of $350 \,m / s$. The phase difference between two displacements at a certain point at times $1 \,m$ apart is ...........
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 $\mathrm{Hz}$.
An observer standing at station observes frequency $219 Hz$ when a train approaches and $184 Hz$ when train goes away from him. If velocity of sound in air is $340\, m/s$, then velocity of train and actual frequency of whistle will be
A tuning fork of known frequency $256\,Hz$ makes $5$ beats per second with the vibrating string of a guitar. The beat frequency decreases to $2$ beats per second when the tension in the guitar string slightly increased. The frequency of the guitar string before increasing the tension was ..... $Hz$
A string of length $1\, m$ and mass $5\, g$ is fixed at both ends. The tension in the string is $8.0\, N$. The string is set into vibration using an external vibrator of frequency $100\, Hz$. The separation between successive nodes on the string is close to .... $cm$