String Open at One End

Q.

Two identical strings X and Z made of the same material have tension $T_x$ and $T_z$ in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio $\frac{T_x}{T_z}$ is:

1. 2.25

2. 1.25

3. 0.44

4. 1.50

Q. If fundamental frequency is $50\text{Hz}$ and next succesive frequencies are $150\text{Hz}$ and $250\text{Hz}$, then which of the following options correctly represents the state of the string?

1. String fixed at both end
2. String fixed at one end & free at other
3. String may be fixed at one end as well as at both ends
4. None of the above

Q. A $4\text{m}$ long rope, having a mass of $40\text{g}$ is fixed at one end and is tied to a light string at the other end. Find the tension in the string if the difference between frequencies of consecutive overtones is $40\text{Hz}$.

1. $1024\text{N}$
2. $512\text{N}$
3. $2048\text{N}$
4. $1000\text{N}$

Q. A horizontal rope of $1\text{m}$ length, having a mass $100\text{g}$, is fixed at one end and is tied to a light string at the other end. Find the frequency and wavelength of the fifth overtone, if the tension in the string is $40\text{N}$.

1. $50\text{Hz},20\text{cm}$
2. $55\text{Hz},36\text{cm}$
3. $110\text{Hz},36\text{cm}$
4. $55\text{Hz},72\text{cm}$

Q. A $1\text{m}$ long horizontal rope, having a mass of $40\text{g}$, is fixed at one end and is tied to a light string at the other end. The tension in the rope is $400\text{N}$. What will be the wavelengths (in $\text{metres}$) in the first and second overtone ?

1. $\frac{3}{4},\frac{3}{4}$
2. $\frac{4}{3},\frac{4}{5}$
3. $\frac{5}{4},\frac{5}{3}$
4. $\frac{4}{5},\frac{4}{3}$

Q. A standing wave is produced in a $10\text{m}$ long string fixed at one end and free at the other end. Find the wavelength of wave, if string is vibrating in its second overtone, and wave velocity is $20\text{m/s}$.

1. $5\text{m}$
2. $4\text{m}$
3. $10\text{m}$
4. $8\text{m}$

Q. A certain string (fixed at one end and free at the other end) can vibrate at several frequencies, the lowest of which is $200\text{Hz}$. What are next two higher frequencies to which it vibrates?

1. $600\text{Hz},1000\text{Hz}$
2. $300\text{Hz},400\text{Hz}$
3. $200\text{Hz},250\text{Hz}$
4. $100\text{Hz},150\text{Hz}$

Q. A standing wave is produced in a $10\text{m}$ long string fixed at one end and free at the other end. Find the wavelength of wave, if string is vibrating in its second overtone, and wave velocity is $20\text{m/s}$.

1. $5\text{m}$
2. $4\text{m}$
3. $10\text{m}$
4. $8\text{m}$

Q. A string of length $10\text{cm}$ fixed at one end and free at another end, has its fundamental frequency half that of second overtone for another string fixed at both ends. What will be the length of string fixed at both ends?
(Assume velocity of wave in both strings is same)

1. $10\text{cm}$
2. $20\text{cm}$
3. $40\text{cm}$
4. $30\text{cm}$

Q. A $4\text{m}$ long rope, having a mass of $40\text{g}$ is fixed at one end and is tied to a light string at the other end. Find the tension in the string if the difference between frequencies of consecutive overtones is $40\text{Hz}$.

1. $1024\text{N}$
2. $512\text{N}$
3. $2048\text{N}$
4. $1000\text{N}$

Q. Wave is travelling on a stretched string fixed at one end as shown in the figure. The resultant force acting on particle at point A is

1. Zero
2. In upward direction
3. In downward direction
4. Can't be determined

Q. Wave is travelling on a stretched string fixed at one end as shown in the figure. The resultant force acting on particle at point A is

1. Zero
2. In upward direction
3. In downward direction
4. Can't be determined