Waves and Vibrations

Wave Speed and Frequency

Wave motion is a fundamental concept in physics, describing the transfer of energy through oscillations. The speed of a wave () is determined by its wavelength () and period () or frequency ():

• Wave speed formula:

• Example: For a wave of length 1.2 m and period 0.48 s, m/s.

Wave on a String

The speed of a wave on a stretched string depends on the tension () and the linear mass density ():

• Formula:

• Linear mass density:

• Example: For a 25 kg rope, 125 m long, kg/m. If N, m/s$.

Standing Waves and Harmonics

Standing waves form when waves reflect and interfere on a string or in a pipe. The frequency of harmonics depends on the length and wave speed:

• Second harmonic frequency:

• Example: For m, m/s, Hz.

Waves in Pipes

Pipes can support standing waves. For a pipe open at both ends, the fundamental frequency is:

• Formula:

• Example: For m, m/s, Hz.

Sound and Intensity

Sound Intensity and Decibels

Sound intensity () is the power per unit area. The loudness is measured in decibels ():

• Intensity:

• Decibel level: , where W/m2

• Example: If W/m2, dB.

Doppler Effect

The Doppler effect describes the change in frequency due to relative motion between source and observer:

• Formula:

• Example: For a whistle moving toward a listener, Hz.

Electrostatics and Electric Fields

Coulomb's Law

The force between two point charges is given by Coulomb's law:

• Formula: , where N·m2/C2

• Example: For C, , m, N, solve for .

Electric Field Strength

The electric field () due to a point charge is:

• Formula:

• Example: For C, m, N/C.

Electric Field Between Plates

For parallel plates, the field is uniform:

• Formula:

• Example: For V, m, V/m.

Motion of Charged Particles

Charged particles in electric fields experience acceleration:

• Formula:

• Example: For C, N/C, mg, m/s2.

Electric Potential and Energy

The change in kinetic energy of a charge accelerated by a potential difference ():

• Formula:

• Example: For a proton accelerated by 4.0 kV, .

Summary Table: Key Equations

Additional info:

• Some questions involve interpreting diagrams of electric field lines and charge arrangements, which are essential for understanding field direction and magnitude.

• Conversions and constants are provided at the end of the document for reference in calculations.