A string is stretched between fixed points separated by $75.0\, cm$. 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 .... $Hz$
AIIMS 2008, Medium
Download our app for free and get started
Given $\frac{\mathrm{nv}}{2 \ell}=315$ and $(\mathrm{n}+1) \frac{\mathrm{v}}{2 \ell}=420$
$\Rightarrow \frac{n+1}{n}=\frac{420}{315} \Rightarrow n=3$
Hence $3 \times \frac{\mathrm{v}}{2 \ell}=315 \Rightarrow \frac{\mathrm{v}}{2 \ell}=105 \mathrm{Hz}$
The lowest resonant frequency is when
$\mathrm{n}=1$
Therefore lowest resonant frequency
$=105 \mathrm{Hz}$
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
- 1An observer starts moving with uniform acceleration $a$ toward a stationary sound source emitting a whistle of frequency $n.$ As the observer approaches source, the apparent frequency, heard by the observer varies with time asView Solution
- 2A tuning fork and a sonometer wire were sounded together and produce $4$ beats per second. When the length of sonometer wire is $95 cm$ or $100 cm,$ the frequency of the tuning fork is ..... $Hz$View Solution
- 3Two opens organ pipes of length $50\, cm$ and $50.5\, cm$ produce three beats. Then, the velocity of sound is ..... $m/s$View Solution
- 4Ultrasonic, Infrasonic and audible waves travel through a medium with speeds ${V_u},\,{V_i}$ and ${V_a}$ respectively, thenView Solution
- 5View SolutionIf vm is the velocity of sound in moist air, vd is the velocity of sound in dry air, under identical conditions of pressure and temperature
- 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
- 7A stationary sound source $'s'$ of frequency $334\,\, Hz$ and a stationary observer $'O'$ are placed near a reflecting surface moving away from the source with velocity $2\,\, m/sec$ as shown in the figure. If the velocity of the sound waves is air is $V = 330\,\, m/sec$, the apparent frequency of the echo is ... $Hz$View Solution
- 8View SolutionA big explosion on the moon cannot be heard on the earth because
- 9Equation of a stationary wave is $y = 10\sin \frac{{\pi x}}{4}\cos 20\pi\, t.$ Distance between two consecutive nodes isView Solution
- 10View SolutionMechanical waves on the surface of a liquid are