A string of length $2 m$ is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of $500 Hz$ then the waves would travel on its with a velocity of ..... $m/s$
Medium
Download our app for free and get started
(c) For string $\lambda = \frac{{2l}}{p}$
where $p =$ No. of loops = Order of vibration
Hence for forth mode $p = 4$
where $p =$ No. of loops = Order of vibration
Hence for forth mode $p = 4$
==> $\lambda = \frac{l}{2}$
Hence $v = n\lambda = 500 \times \frac{2}{2} = 500\,Hz$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A string $2.0\, m$ long and fixed at its end is driven by a $240\, Hz$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency isView Solution
- 2The equation of a wave travelling on a string is $y = 4\sin \frac{\pi }{2}\left( {8t - \frac{x}{8}} \right)$. If $x$ and $y$ are in $cm,$ then velocity of wave isView Solution
- 3A whistle producing sound waves of frequencies $9500\ Hz$ and above is approaching a stationary person with speed $v\ ms^{-1}$. The velocity of sound in air is $300\ ms^{-1}$. If the person can hear frequencies upto a maximum of $10,000\ Hz$, the maximum value of $v$ upto which he can hear whistle is ... $ms^{-1}$View Solution
- 4A granite rod of $60\ cm$ length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7 \times 10^3 $ $kg/m^3$ and its Young's modulus is $9.27 \times 10^{10}$ $Pa$ What will be the fundamental frequency of the longitudinal vibrations .... $kHz$ ?View Solution
- 5The displacement of a particle is given by $y = 5 \times {10^{ - 4}}\sin (100t - 50x)$, where $x$ is in meter and $t$ in sec, find out the velocity of the wave .... $m/sec$View Solution
- 6A motorcyclist is approaching a large wall with a velocity of $90\,km/hr$. A car is chasing him with a velocity of $108\,km/hr$. If the car sounds a horn at $30\,Hz,$ beat frequency heard by motorcyclist is ____ $Hz$ . Take velocity of sound $= 330\,m/s$ .View Solution
- 7$Assertion :$ Sound travels faster in solids than gases.View Solution
$Reason :$ Solids possess greater density than gases. - 8In a Resonance -Coulmn lab experiment to measure the velocity of sound, the first resonance is obtained at a length $l_1$ and the second resonance at a length $l_2$. Then-View Solution
- 9The couple of tuning forks produces $2$ beats in the time interval of $0.4$ seconds. So the beat frequency is .... $Hz$View Solution
- 10The fundamental frequency of a sonometer wire is increases by $6\, Hz$ if its tension is increased by $44\%$, keeping the length constant. The frequency of the wire is ...... $Hz$View Solution