V= λ f
where, V=velocity , λ = wavelength and f= frequency
Netwon’s formula ,
- V= √(B/D)
- B --> Bulk modulus of elasticity
- D---> density of medium
Laplace correction,
- V= √(γP/ρ)
- Y= young’s modulus, ρ is density
Wave Velocity = λ * f
Also, wave speed = w/k w= 2πf k= 2π/λ
y = a sin (wt -kx)
Audible frequency for human ear = 20 Hz to 20 KHz
Velocity in air = 332 m/s
Threshold intensity for human = 10-12 W/m2
Maximum tolerable sound intensity = 120 db
Vt = V0 + 0.61 t ( for small temperature change only)
| I max/ I min = (a1 + a2 / a1 – a2)2= ( √I1 + √I2/√I1-√I2)2 |
Velocity of sound is independent of pressure.
Intensity of wave
I = 2π2f2a2ρV where, f = frequency of wave P0= pressure amplitude
I= P20 / 2ρV
Sound wave do not exhibit polarization because it is longitudinal wave.
| 2π/λ * path difference = phase difference |
>For closed organ pipe
, fundamental frequency f= V/4L
And harmonics goes on odd multiple 1, 3, 5, 7…….
For open organ pipe
fundamental frequency f= V/ 2L
And harmonics goes on multiple of natural number 1, 2,3 ,4…….
Resonance tube
- > formulas
- V= 2f (L2-L1)
- end correction e= (e2 -3L1 )/2
At nodes
pressure and emergency are energy are maximum and displacement is minimum and opposite for antinode.
String case
V = √(T / µ ) where µ = mass per unit length
F= 1/2L * √(T/µ) or f = 1/2L *√(T/ A * ρ)
Others
T1 = n2T ( n = number of times velocity is changed, T = temperature)
To hear echo minimum distance distance is 17m and time should not be more than 0.1 second.
Moist air is lighter than dry air ( ρd >ρm)
For monosallable sound = 1/5 second
For disallable sound = 2/5 second
For trisallable sound = 3/ 5 second
Tuning fork
@ trick ( u f i )
u = unknown , fi = filling , I = increases
this means , when filling is done on unknown tuning fork and then beat increases then required frequency of tuning fork is larger value.
Transverse waves are produced in prongs while longitudinal waves are produced in stem.
Time interval between successive maxima or minima = 1/(f 1 – f 2 )
Length of tuning fork when decreased , frequency increases.
Length of tuning fork when decreased , frequency increases.
If after cutting beats donot change , then original frequency is ( new frequency = beat )
Doppler’s effect
New frequency =( velocity change in observer / velocity change in source ) @ observer is always up in formula
Velocity change is in difference , when velocity of observer or source and sound is in same direction and addition for opposite direction.
When no movement is seen on observer or source only velocity of sound is written.
Eg,
When source and observer are moving towards each other.
- Step 1: Put observer at the top of formula, so check observer first.
- Step 2: Check the direction of observer and velocity of sound. Here they are in opposite direction so they shoulb be added. Put V+V0
- Step 3: Check the velocity of sound (V) and velocity of source (Vs) and put it below in the formula. Put + if opposite direction and '-' if same direction. Here, it is in same direction so put minus. Then you can easily solve the problems.
- Step 4: f ‘ = (V +V0/V –Vs )* f
For reflection from a free boundry, phase change is 0 but compression reflects as rarefaction and vice versa,.
For reflection from a rigid boundry, phase change is π but compression reflects as compression and rarefaction.
Tone -------> sound wave of single frequency.
Note -------> sound wave of many frequency.
Doppler’s effect in light
∆ f /f = V/C OR ∆λ/λ = V/C (where V is velocity and C is velocity of light)
Radar
∆f / f = 2V/C or, ∆λ /λ = 2v/C