Answer:
a)v= 172.7m/s
b)λ [tex]Ф_{1}[/tex] =2.2m
c)λ [tex]Ф_{2}[/tex] = 1.1m
d)f= 78.5 Hz
e)f= 157 Hz
Explanation:
Length 'L'=1.1 m
mass 'm'= 5.9g =>0.0059kg
Tension 'T'= 160N
a)the speed of a wave on strecteed string is given by,
v= √T/μ
where μ is mass per unit length
v= [tex]\sqrt{\frac{T}{m/L} }[/tex] => [tex]\sqrt{\frac{160}{(0.0059)/1.1} }[/tex]
v= 172.7m/s
b)The general formula for the wavelength of the waves that produce one-loop is guven by,
λ = 2L/n
λ [tex]Ф_{1}[/tex] = 2(1.1)/1 =>2.2m
c)the wavelength of the waves that produce two-loop is given by,
λ [tex]Ф_{2}[/tex] = 2(1.1)/2 =>1.1m
d) For the frequency of the waves that produce one-loop waves:
f= n[tex]\frac{v}{2L}[/tex] (n=1)
f=[tex]\frac{172.7}{(2)(1.1)}[/tex] => 78.5 Hz
e)For the frequency of the waves that produce two-loop standing waves:
f= n[tex]\frac{v}{2L}[/tex] (n=2)
f= 2 x [tex]\frac{172.7}{(2)(1.1)}[/tex] => 157 Hz
Answer:
a) 172.77 m/s
b) 2.2 m
c) 1.1 m
d) 78.53 Hz
e) 157.06 Hz
Explanation:
Given that
Length of wire, l = 1.1 m
Mass of wire, m = 5.9 g = 0.0059 kg
Tension of the wire, T = 160 N
a)
v = √(T / μ), where μ = l/m, thus
v = √(T /(m/l))
v = √(160 /(0.0059/1.1))
v = √(160 / 0.00536)
v = √29851
v = 172.77 m/s
b)
λ(1) = 2l / n
λ(1) = (2 * 1.1) / 1
λ(1) = 2.2 m
c)
λ(2) = 2l / n
λ(2) = (2 * 1.1) / 2
λ(2) = 1.1 m
d)
f(1) = n * v/2l
f(2) = 172.77 / (2 * 1.1)
f(2) = 78.53 Hz
e)
f(2) = n * v/2l
f(2) = 2 * 172.77/(2 * 1.1)
f(2) = 157.06 Hz
