How did shortening the length of the spring affect the resonant frequencies? How does this confirm the relationship v = ? f when velocity is constant? And how musical instruments create higher and lower tones. Use a string instrument as an example.

I can't explain above question well....When the wavelength becomes short, it increases its frequency.

For a pair of dice, if the discrete random variable is defined by χ= {█(1 if a=b@max⁡(a,b)if a≠b)┤
(i) Determine the χ; χ(S) (ii) Construct the probability distribution table of χ;f(xi) (iii) Find the expected value χ;E(χ) (v) Variance (vi) Standard deviation (vi) Normal interval for

A baseband signal s(t)=8cos(2000t + 45)V, is wideband FM modulated with carrier amplitude of 40 volts. The index of modulation is beta=3.

a. show the simplified equation of the wideband FM modulation

b. determine wideband FM power using Bessel function table

c. Calculate Kf in the wideband FM modulation equation.

An ideal gas is taken through a complete cycle in three steps: adiabatic expansion with work equal to I25 J, isothermal contraction at 325 K, and increase in pressure at constant volume.

(a) Draw a p-V diagram for the three steps.

(b) How much energy is transferred as heat in step 3, and

(c) is it transferred to or from the gas?

A semiconductor diode, the forward and reverse characteristics of which can be considered ideal, is used in a half-wave rectifier circuit supplying a resistive load of 1000Ω. If the r.m.s. value of the sinusoidal supply voltage is 230 V determine: (a) the peak diode current; (b) the mean diode current; (c) the r.m.s. diode current; (d) the power dissipated in the load

In each of the following situations, Emma is in the exact center of a glass-sided freight car speeding to the right at a very high speed v relative to you. For each question, explain your reasoning.

1. Emma has a flashlight in each hand and directs them at the front and rear ends of the freight car. She then switches the flashlights on at the same time.

   1. In Emma

Two moles of nitrogen gas at 25°C, confined within a cylinder by a piston maintaining a constant pressure of 1 atm, is heated with 5.30 kJ of energy. Assume all the energy is used to do work of expansion of the gas at 1 atm. What will be the final temperature of the gas? Recall ∆H = ∆E + P∆V and watch your units!

A 40.0-uF capacitor is connected to a 50.0-ohm resistor and a generator whose rms output is 30.0 V at 60.0 Hz.

Find...

A) the rms current circuit

B) the rms voltage drop across the resistor

C) the rms voltage drop across the capacitor

D) and the phase angle for the circuit

Please Explain how to get these answers, Thankyou

The parity operator P is defined by

ˆ Pψ (x) =ψ (−x)

for any function ψ(x).

(a) Prove that this parity operator P is Hermitian.

(b) Find its eigenvalues, and also its eigenfunctions (in terms of ψ(x)).

(c) Prove that this parity operator commutes with the Hamiltonian when potential V(x) is an even function.

II. Discuss the planning feature of garden at industrial estate. III. Explain the merits and demerits of Green roofs. IV. State types of Mughal gardens along with their landscape planning citing examples V. Discuss the role of children’s play area in the city and elaborate design considerations and element used for different age groups (5 Marks