Aim
To study the relation between the frequency and the length of a given wire under constant tension using a sonometer.
Apparatus/Materials Required
- A set of eight tuning forks
- A sonometer
- Seven ½ kg slotted weights
- Paper rider
- Rubber Pad
- Screw gauge
- Metre-scale
- ½ kg hanger
Diagram
Theory
If the stretched wire vibrates in resonance with the tuning fork with a frequency v, then the string also manifests the same frequency v.
Considering that the string is of length l with diameter D and a density ρ and length l, then the frequency of the string is given by the equation,
(v=frac{1}{lD}sqrt{frac{T}{pi ho }})From the above equation, we know that
(vpropto l)vl = constant
The graph between v and l will be a hyperbola while the graph between v and 1/l will be a straight line.
The relation between the length (l) and tension (T) from the above equation, is given as follows:
(sqrt{frac{T}{l}}=constant) (sqrt{T}propto l) (Tpropto l^2)A graph between T and l2 will be a straight line
Procedure
- Place the sonometer on the table as shown in the figure.
- Oil the pulley to make it frictionless
- Put suitable maximum weight to the hanger
- Move the wooden bridge P outward to include the maximum length of wire AB between them.
- Pick the tuning fork of the least frequency from the set. Make it vibrate by striking its prong on a rubber pad. Bring the fork close to the ear.
- Pluck the wire AB from the middle and leave it to vibrate.
- Listen to the sound produced by both the tuning fork and the wire and judge which has less frequency.
- Since the long wire may have less frequency move the bridges inward and check the frequencies again.
- Go on decreasing the length of the wire till the frequency of the wire becomes equal to the frequency of the tuning fork.
- Place an inverted V-shaped paper rider in the middle of the wire AB. Vibrate the tuning fork and touch the lower end of its handle with a sonometer board. The wire AB vibrates due to resonance and the paper rider falls.
- Note the length of the wire AB between the edges of two bridges and record it in the ‘length decreasing’ column.
- Bring the bridges closer and adjust the length of the wire by increasing little by little till the rider falls.
- Note the length of the wire and record it in ‘length increasing column.’
- Take the rest of the five tuning forks, and one by one, in the order of increasing frequency repeat steps 5 to 13.
- Record the observations as given below.
Observations
Constant tension on the wire, T = _____ kg.
| Serial No of observations | Frequency of tuning fork used v (Hz) | Resonant length of wire | 1/l cm–1 | ||
| Length increasing (l1) | Length decreasing(l2) | (frac{l_1+l_2}{2}) | |||
Table for frequency and length
Calculations
- Find the mean length l.
- Determine 1/l
- Plot a graph between v and l, with v along the x-axis and l along the y-axis.
- Now, plot a graph between v and 1/l, with v along the x-axis and 1/l along the y-axis. The graph is a straight line as shown below.
Result
From the graph, it can be concluded that vl = constant and (vpropto frac{1}{l}).
Viva Voce
1.What is the principle involved in sonometer?
Answer: Resonance is the principle involved in the sonometer.
2. Which type of waves are produced in the sonometer experiment?
Answer: Transverse waves are produced in the sonometer experiment.
3. What is the relationship between frequency and the length of a given wire under constant tension?
Answer: The relationship between the frequency and the length of a given wire under constant tension is given by the equation
(v=frac{1}{lD}sqrt{frac{T}{pi ho }})Stay tuned with CoolGyan’S to get the latest notification on CBSE along with CBSE syllabus, sample papers, marking scheme, and more.
