Given: Frequency of wave = 100 Hz, Distance of node from fixed end = 10 cm

To find: Speed of wave (incident and reflected)

Assumption: The string is assumed to be homogeneous, i.e., the properties of the string do not change along its length.

Formula: For a wave travelling along a string, the speed of the wave is given by the formula:

v = √(T/μ)

where,
v = speed of wave
T = tension in the string
μ = linear mass density of the string

Analysis:

1. Finding the wavelength of the wave:

We know that the frequency of the wave is 100 Hz. The wave equation is given by:

v = λf

where,
v = speed of wave
λ = wavelength of wave
f = frequency of wave

Rearranging the equation, we get:

λ = v/f

Substituting the values, we get:

λ = v/100

2. Finding the tension in the string:

When the wave reaches the fixed end of the string, it gets reflected back. At the point of reflection, a node is formed. This means that the displacement of the string at that point is zero. The displacement of a string is given by the equation:

y(x,t) = A sin(kx - ωt)

where,
y = displacement of the string
A = amplitude of the wave
k = wave number
x = position along the string
t = time
ω = angular frequency

At the point of reflection, x = 10 cm and y = 0. Hence, we get:

0 = A sin(kx - ωt)

Since sinθ = 0 when θ = nπ, where n is an integer, we get:

kx - ωt = nπ

At the point of reflection, the wave is travelling in the opposite direction. Hence, the wave equation becomes:

y(x,t) = A sin(kx + ωt)

Substituting the value of x = 10 cm and k = 2π/λ, we get:

A sin(2π/λ * 10 - ωt) = 0

Simplifying, we get:

2π/λ * 10 - ωt = nπ

Substituting the value of λ, we get:

20π - ωt = nπ

Since the wave is travelling in the opposite direction, the angular frequency becomes negative. Hence, we get:

20π + ωt = nπ

At the point of reflection, the wave is reflected with the same speed as the incident wave. Hence, the tension in the string remains the same before and after reflection. Let the tension in the string be T.

3. Finding the linear mass density of the string:

The linear mass density of the string is given by the formula:

μ = m/l

where,
m = mass of the string
l = length of the string

Assuming a uniform cross-sectional area of the string, we can write:

m = ρAl

where,
ρ = density of the string
A = cross-sectional area of the string
l = length of the string

Substituting the value of m in the formula for linear mass density, we get:

μ = ρA

where,
A = cross-sectional area of the string

4. Finding the