The correct answer is 0.004 s. Explanation & Key Takeaways: • The time period of a wave is the reciprocal of its frequency. It is calculated using the formula: Time Period (T) = 1 / Frequency (f) • The given frequency of the sound wave is 250 Hz. Substituting this into the formula: T = 1 / 250 = 0.004 seconds. • Therefore, the time period of the sound wave is 0.004 seconds. • The unit of frequency is Hertz (Hz), which represents the number of cycles per second. The unit of time period is seconds (s). • This calculation confirms that the correct option is 0.004 s, which corresponds to Option 1. Related Concepts: • Frequency and Time Period Relationship: • Frequency (f) and time period (T) are inversely proportional. This means as frequency increases, the time period decreases, and vice versa. • The mathematical expression for their relationship is: T = 1 / f or f = 1 / T. • Definition of Frequency: • Frequency is the number of complete oscillations or cycles a wave completes in one second. • It is measured in Hertz (Hz). For example, 1 Hz = 1 cycle per second. • Definition of Time Period: • The time period is the time taken to complete one oscillation or cycle of a wave. • It is measured in seconds (s). • Applications of Frequency and Time Period: • These concepts are widely used in fields like acoustics, electronics, and signal processing. • In sound waves, frequency determines the pitch of the sound, while the time period provides insights into the wave's periodicity. • Real-life Examples: • A guitar string vibrating at 440 Hz has a time period of approximately 0.00227 seconds. • The human ear can typically hear frequencies ranging from 20 Hz to 20,000 Hz. Important Notes: • Speed of Sound: • The speed of sound in air is approximately 343 m/s at room temperature (20°C). • The speed depends on factors like medium, temperature, and pressure. • Wavelength and Frequency: • Wavelength (λ) is inversely proportional to frequency when the speed of the wave is constant: λ = v / f, where v is the speed of the wave. • Higher frequency waves have shorter wavelengths. • Practical Use: • Frequency and time period calculations are vital in designing musical instruments, speakers, and communication devices. • They are also crucial in medical imaging techniques like ultrasound.